Journal articles: 'Bounded jumps'

1

Dembo, Amir. "Moderate Deviations for Martingales with Bounded Jumps." Electronic Communications in Probability 1 (1996): 11–17. http://dx.doi.org/10.1214/ecp.v1-973.

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HOLLAND, DAVID M., RODOLFO R. ROSALES, DAN STEFANICA, and ESTEBAN G. TABAK. "Internal hydraulic jumps and mixing in two-layer flows." Journal of Fluid Mechanics 470 (October 31, 2002): 63–83. http://dx.doi.org/10.1017/s002211200200188x.

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Internal hydraulic jumps in two-layer flows are studied, with particular emphasis on their role in entrainment and mixing. For highly entraining internal jumps, a new closure is proposed for the jump conditions. The closure is based on two main assumptions: (i) most of the energy dissipated at the jump goes into turbulence, and (ii) the amount of turbulent energy that a stably stratified flow may contain without immediately mixing further is bounded by a measure of the stratification. As a consequence of this closure, surprising bounds emerge, for example on the amount of entrainment that may take place at the location of the jump. These bounds are probably almost achieved by highly entraining internal jumps, such as those likely to develop in dense oceanic over flows. The values obtained here are in good agreement with the existing observations of the spatial development of oceanic downslope currents, which play a crucial role in the formation of abyssal and intermediate waters in the global ocean.

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KANIGOWSKI, ADAM. "Ratner’s property for special flows over irrational rotations under functions of bounded variation." Ergodic Theory and Dynamical Systems 35, no. 3 (October 11, 2013): 915–34. http://dx.doi.org/10.1017/etds.2013.74.

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AbstractWe consider special flows over the rotation by an irrational$\alpha $under the roof functions of bounded variation without continuous, singular part in the Lebesgue decomposition and sum of jumps not equal to zero. We show that all such flows are weakly mixing. Under the additional assumption that$\alpha $has bounded partial quotients, we study the weak Ratner property. We establish this property whenever an additional condition (stable under sufficiently small perturbations) on the set of jumps is satisfied. While it is a classical result that the flows under consideration are not mixing, one more condition on the set of jumps turns out to be sufficient to obtain the absence of partial rigidity, hence mild mixing of such flows.

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KATE, R. P., P. K. DAS, and SUMAN CHAKRABORTY. "Hydraulic jumps due to oblique impingement of circular liquid jets on a flat horizontal surface." Journal of Fluid Mechanics 573 (February 2007): 247–63. http://dx.doi.org/10.1017/s0022112006003818.

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An obliquely inclined circular water jet, impinging on a flat horizontal surface, confers a series of hydraulic jump profiles, pertaining to different jet inclinations and jet velocities. These jump profiles are non-circular, and can be broadly grouped into two categories, based on the angle of jet inclination, φ, made with horizontal. Jumps corrosponding to the range (25° < φ≤ 90°) are observed to be bounded by smooth curves, whereas those corresponding to φ≤ 25° are characterized by distinct corners. The present work attempts to find a geometric and hydrodynamic characterization of the spatial patterns formed as a consequence of such non-circular hydraulic jump profiles. Flow-visualization experiments are conducted to depict the shape of demarcating boundaries between supercritical and subcritical flows, and the corresponding radial jump locations are obtained. Theoretical calculations are also executed to obtain the radial locations of the jumps with geometrically smooth profiles. Comparisons are subsequently made between the theoretical predictions and the experimental observations, and a good agreement between these two can be observed. Jumps with corners, however, turn out to be comprised of strikingly contrasting profiles, which can be attributed to the ‘jump–jet’ interaction and the ‘jump-jump’ interaction mechanisms. A phenomenological explanation is also provided, by drawing an analogy from the theory of shock-wave interactions.

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ADOUANI, ABDELHAMID, and HABIB MARZOUGUI. "Singular measures for classP-circle homeomorphisms with several break points." Ergodic Theory and Dynamical Systems 34, no. 2 (April 2012): 423–56. http://dx.doi.org/10.1017/etds.2012.133.

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AbstractLetfbe a classP-homeomorphism of the circle with break point singularities, that is, differentiable except at some singular points where the derivative has a jump. Letfhave irrational rotation number andDfbe absolutely continuous on every continuity interval ofDf. We prove that if the product of thef-jumps along any subset of break points is distinct from 1 then the invariant measureμfis singular with respect to the Haar measure. This result generalizes previous results obtained by Dzhalilov and Khanin, Dzhalilov, Akhadkulov, Dzhalilov–Liousse and Mayer. Moreover, we prove that if the rotation numberρ(f) is irrational of bounded type then (a) if the product of thef-jumps on some orbit is distinct from 1 then the invariant measureμfis singular with respect to the Haar measurem, and (b) if the product of thef-jumps on each orbit is equal to 1 andD2f∈Lp(S1) for somep>1 thenμfis equivalent to the Haar measure.

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Zhang, Yujie, Xiujuan Liu, Junxia Jiang, and Yongshan Xiao. "Dissipativity-based resilient asynchronous control for Markov jump systems with sector-bounded nonlinearities." Transactions of the Institute of Measurement and Control 40, no. 9 (May 9, 2018): 2821–30. http://dx.doi.org/10.1177/0142331218765295.

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The resilient asynchronous dissipative control problem for Markov jump systems with sector-bounded nonlinearities in the discrete-time domain are examined in this study. The jumps between the system modes and controller modes are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the asynchronous jumps to different degrees that are also mode-dependent. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system and by constructing a new multiple Lyapunov function, sufficient conditions regarding the existence of desired resilient asynchronous dissipative controllers are obtained in terms of linear matrix inequalities, which ensure the closed-loop system is stochastically stable and strictly dissipative. The designed controller can tolerate additive uncertainties in the controller gain matrix, which results from controller implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.

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7

Chaikovs'kyi, A., and O. Lagoda. "Bounded solutions of a difference equation with finite number of jumps of operator coefficient." Carpathian Mathematical Publications 12, no. 1 (June 28, 2020): 165–72. http://dx.doi.org/10.15330/cmp.12.1.165-172.

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We study the problem of existence of a unique bounded solution of a difference equation with variable operator coefficient in a Banach space. There is well known theory of such equations with constant coefficient. In that case the problem is solved in terms of spectrum of the operator coefficient. For the case of variable operator coefficient correspondent conditions are known too. But it is too hard to check the conditions for particular equations. So, it is very important to give an answer for the problem for those particular cases of variable coefficient, when correspondent conditions are easy to check. One of such cases is the case of piecewise constant operator coefficient. There are well known sufficient conditions of existence and uniqueness of bounded solution for the case of one jump. In this work, we generalize these results for the case of finite number of jumps of operator coefficient. Moreover, under additional assumption we obtained necessary and sufficient conditions of existence and uniqueness of bounded solution.

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8

Chen, Guici, and Yi Shen. "Robust ReliableH∞Control for Nonlinear Stochastic Markovian Jump Systems." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/431576.

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The robust reliableH∞control problem for a class of nonlinear stochastic Markovian jump systems (NSMJSs) is investigated. The system under consideration includes Itô-type stochastic disturbance, Markovian jumps, as well as sector-bounded nonlinearities and norm-bounded stochastic nonlinearities. Our aim is to design a controller such that, for possible actuator failures, the closed-loop stochastic Markovian jump system is exponential mean-square stable with convergence rateαand disturbance attenuationγ. Based on the Lyapunov stability theory and Itô differential rule, together with LMIs techniques, a sufficient condition for stochastic systems is first established in Lemma 3. Then, using the lemma, the sufficient conditions of the solvability of the robust reliableH∞controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.

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9

Shi, Peng, Carlos E. De Souza, and Lihua Xie. "Bounded real lemma for linear systems with finite discrete jumps." International Journal of Control 66, no. 1 (January 1997): 145–60. http://dx.doi.org/10.1080/002071797224865.

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10

Bujtás, Csilla, and Zsolt Tuza. "Color-bounded hypergraphs, VI: Structural and functional jumps in complexity." Discrete Mathematics 313, no. 19 (October 2013): 1965–77. http://dx.doi.org/10.1016/j.disc.2012.09.020.

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11

Mounaix, Philippe, and Grégory Schehr. "First gap statistics of long random walks with bounded jumps." Journal of Physics A: Mathematical and Theoretical 50, no. 18 (March 31, 2017): 185001. http://dx.doi.org/10.1088/1751-8121/aa65f2.

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12

Xing, Mei. "Existence Conditions of Super-Replication Cost in a Multinomial Model." Journal of Mathematics Research 9, no. 4 (July 24, 2017): 185. http://dx.doi.org/10.5539/jmr.v9n4p185.

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This paper gives a theorem for the continuous time super-replication cost of European options in an unbounded multinomial market. An approximation multinomial scheme is put forward on a finite time interval [0,1] corresponding to a pure jump Lévy model with unbounded jumps. Under the assumption that the expected underlying stock price at time 1 is bounded, the limit of the sequence of the super-replication cost in a multinomial model is proved to be greater than or equal to an optimal control problem. Furthermore, it is discussed that the existence conditions of a super-replication cost and a liquidity premium for the multinomial model. This paper concentrates on a multinomial tree with unbounded jumps, which can be seen as an extension of the work of (Xing, 2015). The super-replication cost and the liquidity premium under the variance gamma model and the normal inverse Gaussian model are calculated and illustrated.

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13

Jo, Gwanghyun, and Do Y. Kwak. "Enriched P1-Conforming Methods for Elliptic Interface Problems with Implicit Jump Conditions." Advances in Mathematical Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9891281.

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We develop a numerical method for elliptic interface problems with implicit jumps. To handle the discontinuity, we enrich usual P1-conforming finite element space by adding extra degrees of freedom on one side of the interface. Next, we define a new bilinear form, which incorporates the implicit jump conditions. We show that the bilinear form is coercive and bounded if the penalty term is sufficiently large. We prove the optimal error estimates in both energy-like norm and L2-norm. We provide numerical experiments. We observe that our scheme converges with optimal rates, which coincides with our error analysis.

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14

Jacobsen, Martin. "Exit times for a class of random walks exact distribution results." Journal of Applied Probability 48, A (August 2011): 51–63. http://dx.doi.org/10.1239/jap/1318940455.

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For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also determined and the paper concludes with exact distribution results concerning exits from bounded intervals. The proofs use simple martingale techniques together with some classical expansions of polynomials and Rouché's theorem from complex function theory.

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Jacobsen, Martin. "Exit times for a class of random walks exact distribution results." Journal of Applied Probability 48, A (August 2011): 51–63. http://dx.doi.org/10.1017/s0021900200099125.

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For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also determined and the paper concludes with exact distribution results concerning exits from bounded intervals. The proofs use simple martingale techniques together with some classical expansions of polynomials and Rouché's theorem from complex function theory.

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16

Chaikovs’kyi, Andrii, and Oksana Lagoda. "Bounded solutions of a second order difference equation with jumps of operator coefficient." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 2 (2022): 57–61. http://dx.doi.org/10.17721/1812-5409.2022/2.7.

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We study the problem of existence of a unique bounded solution of a difference equation of the second order with a variable operator coefficient in a Banach space. In the case of a finite number of jumps of an operator coefficient necessary and sufficient conditions are obtained.

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17

Kuznetsov, A., and X. Peng. "On the Wiener–Hopf factorization for Lévy processes with bounded positive jumps." Stochastic Processes and their Applications 122, no. 7 (July 2012): 2610–38. http://dx.doi.org/10.1016/j.spa.2012.04.014.

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18

Sason, Igal. "Tightened exponential bounds for discrete-time conditionally symmetric martingales with bounded jumps." Statistics & Probability Letters 83, no. 8 (August 2013): 1928–36. http://dx.doi.org/10.1016/j.spl.2013.04.015.

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19

Kvernadze, George. "Determination of the Jumps of a Bounded Function by Its Fourier Series." Journal of Approximation Theory 92, no. 2 (February 1998): 167–90. http://dx.doi.org/10.1006/jath.1997.3125.

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20

Goater, Alexander J. N., and Andrew J. Hogg. "Bounded dam-break flows with tailwaters." Journal of Fluid Mechanics 686 (September 27, 2011): 160–86. http://dx.doi.org/10.1017/jfm.2011.317.

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AbstractThe gravitationally driven collapse of a reservoir into an initially stationary layer of fluid, termed the tailwater, is studied using the nonlinear shallow water equations. The motion is tackled using the hodograph transformation of the governing equation which allows the solutions for velocity and depth of the shallow flowing layer to be constructed by analytical techniques. The front of the flow emerges as a bore across which the depth of the fluid jumps discontinuously to the tailwater depth. The speed of the front is initially constant, but progressively slows once the finite extent of the reservoir begins to influence the motion. There then emerges a variety of phenomena depending upon the depth of the tailwater relative to the initial depth of the reservoir. Provided that the tailwater is sufficiently deep, a region of quiescent fluid emerges adjacent to the rear wall of the reservoir, followed by a region within which the velocity is negative. Also it is shown that for non-vanishing tailwater depths, continuous solutions for the velocity and height of the flowing layer breakdown after a sufficient period and develop an interior bore, the location and time of inception of which are calculated directly from quasi-analytical solutions.

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21

Horodnii, M. F., and V. P. Kravets. "Bounded Solutions of a Second-Order Difference Equation with Jumps of Operator Coefficients." Ukrainian Mathematical Journal 73, no. 3 (August 2021): 391–98. http://dx.doi.org/10.1007/s11253-021-01932-z.

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22

Kesten, Harry. "A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps." Advances in Applied Probability 27, no. 3 (September 1995): 652–91. http://dx.doi.org/10.2307/1428129.

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We consider positive matrices Q, indexed by {1,2, …}. Assume that there exists a constant 1 L < ∞ and sequences u1< u2< · ·· and d1d2< · ·· such that Q(i, j) = 0 whenever i < ur < ur + L < j or i > dr + L > dr > j for some r. If Q satisfies some additional uniform irreducibility and aperiodicity assumptions, then for s > 0, Q has at most one positive s-harmonic function and at most one s-invariant measure µ. We use this result to show that if Q is also substochastic, then it has the strong ratio limit property, that is for a suitable R and some R–1-harmonic function f and R–1-invariant measure µ. Under additional conditions µ can be taken as a probability measure on {1,2, …} and exists. An example shows that this limit may fail to exist if Q does not satisfy the restrictions imposed above, even though Q may have a minimal normalized quasi-stationary distribution (i.e. a probability measure µ for which R–1µ = µQ).The results have an immediate interpretation for Markov chains on {0,1,2, …} with 0 as an absorbing state. They give ratio limit theorems for such a chain, conditioned on not yet being absorbed at 0 by time n.

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Kesten, Harry. "A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps." Advances in Applied Probability 27, no. 03 (September 1995): 652–91. http://dx.doi.org/10.1017/s0001867800027105.

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We consider positive matricesQ,indexed by {1,2, …}. Assume that there exists a constant 1L <∞ and sequencesu1< u2< · ··andd1d2< · ··such thatQ(i, j) = 0 wheneveri<ur< ur+L < jori > dr+ L > dr> jfor somer. IfQsatisfies some additional uniform irreducibility and aperiodicity assumptions, then fors> 0,Qhas at most one positives-harmonic function and at most ones-invariant measureµ.We use this result to show that ifQis also substochastic, then it has the strong ratio limit property, that isfor a suitableRand someR–1-harmonic functionfandR–1-invariant measureµ.Under additional conditionsµcan be taken as a probability measure on {1,2, …} andexists. An example shows that this limit may fail to exist ifQdoes not satisfy the restrictions imposed above, even thoughQmay have a minimal normalized quasi-stationary distribution (i.e. a probability measureµfor whichR–1µ = µQ).The results have an immediate interpretation for Markov chains on {0,1,2, …} with 0 as an absorbing state. They give ratio limit theorems for such a chain, conditioned on not yet being absorbed at 0 by timen.

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Horodnii, M. F., and I. V. Honchar. "On Bounded Solutions of a Difference Equation with Jumps of the Operator Coefficient." Journal of Mathematical Sciences 229, no. 4 (January 24, 2018): 403–11. http://dx.doi.org/10.1007/s10958-018-3685-4.

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25

Becherer, Dirk. "Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging." Annals of Applied Probability 16, no. 4 (November 2006): 2027–54. http://dx.doi.org/10.1214/105051606000000475.

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26

Wang, Hua-Ming. "Law of Large Numbers for Random Walk with Unbounded Jumps and Birth and Death Process with Bounded Jumps in Random Environment." Journal of Theoretical Probability 31, no. 2 (December 18, 2016): 619–42. http://dx.doi.org/10.1007/s10959-016-0731-3.

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Todd, M. D., and L. N. Virgin. "An Experimental Verification of Basin Metamorphoses in A Nonlinear Mechanical System." International Journal of Bifurcation and Chaos 07, no. 06 (June 1997): 1337–57. http://dx.doi.org/10.1142/s0218127497001060.

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This paper describes bifurcations and the basin boundary metamorphoses that give rise to post-fold outcome indeterminacy from a primarily experimental perspective. A gravity-loaded cart-and-track system is constrained to mimic the twin-well, single-degree-of-freedom Duffing oscillator. Of primary interest is the study of how motion, initially contained within a single well, "spills over" into the adjacent well. Although this system is globally bounded, it retains the same generic features of the single-well canonical escape equation. Using time-embedded coordinates, the technique of stochastic interrogation is used to generate the initial condition maps at three different forcing levels corresponding to three different regimes of post-fold outcomes. These three regions are characterized, respectively, by smooth basin boundaries with safe jumps to resonance, fractal basin boundaries with jumps that may or may not restabilize on to the resonant attractor, and eroded basins with unsafe jumps leading to escape from the local well. This experiment successfully replicates much of the subtle global behavior observed in numerical simulations.

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Accardi, L., S. Hachicha, and H. Ouerdiane. "Generic Quantum Markov Semigroups: the Fock Case." Open Systems & Information Dynamics 12, no. 04 (December 2005): 385–99. http://dx.doi.org/10.1007/s11080-005-4488-x.

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We introduce the class of generic quantum Markov semigroups. Within this class we study the class corresponding to the Fock case which is further split into four subclasses each of which contains both bounded and unbounded generators, depending on some global characteristics of the intensities of jumps. For the first two of these classes we find an explicit solution which reduces the problem of finding the quantum semigroup to the calculation of two classical semigroups, one of which is diagonal (in a suitable basis) and the other one is triangular (in the same basis). In the bounded case our formula gives the unique solution. In the unbounded case it gives one solution, which we conjecture to be the minimal one.

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Biermé, Hermine, and Agnès Desolneux. "A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps." Journal of Applied Probability 49, no. 1 (March 2012): 100–113. http://dx.doi.org/10.1239/jap/1331216836.

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We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

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Biermé, Hermine, and Agnès Desolneux. "A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps." Journal of Applied Probability 49, no. 01 (March 2012): 100–113. http://dx.doi.org/10.1017/s0021900200008883.

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We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

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Nehaniv, Chrystopher L., and John L. Rhodes. "The Evolution and Understanding of Hierarchical Complexity in Biology from an Algebraic Perspective." Artificial Life 6, no. 1 (January 2000): 45–67. http://dx.doi.org/10.1162/106454600568311.

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We develop the rigorous notion of a model for understanding state transition systems by hierarchical coordinate systems. Using this we motivate an algebraic definition of the complexity of biological systems, comparing it to other candidates such as genome size and number of cell types. We show that our complexity measure is the unique maximal complexity measure satisfying a natural set of axioms. This reveals a strong relationship between hierarchical complexity in biological systems and the area of algebra known as global semigroup theory. We then study the rate at which hierarchical complexity can evolve in biological systems assuming evolution is “as slow as possible” from the perspective of computational power of organisms. Explicit bounds on the evolution of complexity are derived showing that, although the evolutionary changes in hierarchical complexity are bounded, in some circumstances complexity may more than double in certain “genius jumps” of evolution. In fact, examples show that our bounds are sharp. We sketch the structure where such complexity jumps are known to occur and note some similarities to previously identified mechanisms in biological evolutionary transitions. We also address the question of, How fast can complexity evolve over longer periods of time? Although complexity may more than double in a single generation, we prove that in a smooth sequence of t “inclusion” steps, complexity may grow at most from N to .N C 1/t C N, a linear function of number of generations t, while for sequences of “mapping” steps it increases by at most t. Thus, despite the fact that there are major transitions in which complexity jumps are possible, over longer periods of time, the growth of complexity may be broken into maximal intervals on which it is bounded above in the manner described.

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Applebaum, David, and Stefan Blackwood. "The Kalman-Bucy filter for integrable Lévy processes with infinite second moment." Journal of Applied Probability 52, no. 3 (September 2015): 636–48. http://dx.doi.org/10.1239/jap/1445543837.

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We extend the Kalman-Bucy filter to the case where both the system and observation processes are driven by finite dimensional Lévy processes, but whereas the process driving the system dynamics is square-integrable, that driving the observations is not; however it remains integrable. The main result is that the components of the observation noise that have infinite variance make no contribution to the filtering equations. The key technique used is approximation by processes having bounded jumps.

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Applebaum, David, and Stefan Blackwood. "The Kalman-Bucy filter for integrable Lévy processes with infinite second moment." Journal of Applied Probability 52, no. 03 (September 2015): 636–48. http://dx.doi.org/10.1017/s0021900200113348.

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We extend the Kalman-Bucy filter to the case where both the system and observation processes are driven by finite dimensional Lévy processes, but whereas the process driving the system dynamics is square-integrable, that driving the observations is not; however it remains integrable. The main result is that the components of the observation noise that have infinite variance make no contribution to the filtering equations. The key technique used is approximation by processes having bounded jumps.

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MAUME-DESCHAMPS, VÉRONIQUE. "Correlation decay for Markov maps on a countable state space." Ergodic Theory and Dynamical Systems 21, no. 1 (February 2001): 165–96. http://dx.doi.org/10.1017/s0143385701001110.

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We estimate the decay of correlations for some Markov maps on a countable state space. A necessary and sufficient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non-quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of finitely many cylinders. Estimates are given for some non-uniformly expanding maps and for maps with bounded jumps.

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Loewe, Matthias, Heinrich Matzinger, and Franz Merkl. "Reconstructing a Multicolor Random Scenery seen along a Random Walk Path with Bounded Jumps." Electronic Journal of Probability 9 (2004): 436–507. http://dx.doi.org/10.1214/ejp.v9-206.

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Ding, Liang, Haibo Gao, Kerui Xia, Zhen Liu, Jianguo Tao, and Yiqun Liu. "Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints." Journal of Applied Mathematics 2012 (2012): 1–24. http://dx.doi.org/10.1155/2012/414315.

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The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques.

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Fan, Yingjie, Zhongliang Wei, and Meixuan Li. "Switching-Jumps-Dependent Quasi-Synchronization Criteria for Fractional-Order Memrisive Neural Networks." Fractal and Fractional 7, no. 1 (December 24, 2022): 12. http://dx.doi.org/10.3390/fractalfract7010012.

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This paper investigates the switching-jumps-dependent quasi-synchronization issue for fractional-order memristive neural networks (FMNNs). First, a simplied linear feedback controller is applied. Then, in terms of several fractional order differential inequalities and two kinds of Lyapunov functions, two quasi-synchronization criteria expressed by linear matrix inequality (LMI)-based form and algebraic form are established, respectively. Meanwhile, the co-designed scheme for error bound and control gain is established. Compared with the previous quasi-synchronization results, a strong assumption that the system states must be bounded is removed. Finally, some simulation examples are carried out to display the feasibility and validity of the proposed analysis methods.

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Acerbi, Emilio, and Domenico Mucci. "Curvature-dependent energies: a geometric and analytical approach." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 3 (February 27, 2017): 449–503. http://dx.doi.org/10.1017/s0308210516000202.

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We consider the total curvature of graphs of curves in high-codimension Euclidean space. We introduce the corresponding relaxed energy functional and prove an explicit representation formula. In the case of continuous Cartesian curves, i.e. of graphs cu of continuous functions u on an interval, we show that the relaxed energy is finite if and only if the curve cu has bounded variation and finite total curvature. In this case, moreover, the total curvature does not depend on the Cantor part of the derivative of u. We treat the wider class of graphs of one-dimensional functions of bounded variation, and we prove that the relaxed energy is given by the sum of the length and total curvature of the new curve obtained by closing the holes in cu generated by jumps of u with vertical segments.

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ALLAJ, ERINDI. "IMPLICIT TRANSACTION COSTS AND THE FUNDAMENTAL THEOREMS OF ASSET PRICING." International Journal of Theoretical and Applied Finance 20, no. 04 (April 27, 2017): 1750024. http://dx.doi.org/10.1142/s0219024917500248.

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This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having cádlág (right-continuous with left limits) and cáglád (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, cádlág and cáglád predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to cáglád predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and nonlinear in the order size.

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ADOUANI, ABDELHAMID, and HABIB MARZOUGUI. "Non-rigidity for circle homeomorphisms with several break points." Ergodic Theory and Dynamical Systems 39, no. 9 (November 28, 2017): 2305–31. http://dx.doi.org/10.1017/etds.2017.121.

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In this work, we consider two class $P$-homeomorphisms, $f$ and $g$, of the circle with break point singularities, that are differentiable maps except at some singular points where the derivative has a jump. Assume that they have the same irrational rotation number of bounded type and that the derivatives $\text{Df}$ and $\text{Dg}$ are absolutely continuous on every continuity interval of $\text{Df}$ and $\text{Dg}$, respectively. We show that if $f$ and $g$ are not break-equivalent, then any topological conjugating $h$ between $f$ and $g$ is a singular function, i.e., it is continuous on the circle, but $\text{Dh}(x)=0$ almost everywhere (a.e.) with respect to the Lebesgue measure. In particular, this result holds under some combinatorial assumptions on the jumps at break points. It also generalizes previous results obtained for one and two break points and complements that of Cunha–Smania which was established for break equivalence.

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41

Su, Xiaoming, and Adiya Bao. "Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/950685.

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The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

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Yan, Lixu, and Yongqiang Fu. "Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises." Fractal and Fractional 5, no. 2 (April 12, 2021): 30. http://dx.doi.org/10.3390/fractalfract5020030.

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In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild solutions. In particular, approximate strategy is used to obtain the existence of mild solutions for the problem with linear fractional noises; fixed point theorem is used to achieve the existence of mild solutions for the problem with nonlinear fractional noises. Finally, the approximate controllability of the problems with linear and nonlinear fractional noises is proved by the property of mild solutions.

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Champagnat, Nicolas, and Denis Villemonais. "Uniform convergence of conditional distributions for absorbed one-dimensional diffusions." Advances in Applied Probability 50, no. 01 (March 2018): 178–203. http://dx.doi.org/10.1017/apr.2018.9.

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Abstract In this paper we study the quasi-stationary behavior of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. An important tool is provided by one-dimensional strict local martingale diffusions coming down from infinity. We prove, under mild assumptions, that their expectation at any positive time is uniformly bounded with respect to the initial position. We provide several examples and extensions, including the sticky Brownian motion and some one-dimensional processes with jumps.

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44

Foss, Sergey, and Masakiyo Miyazawa. "Two-node fluid network with a heavy-tailed random input: the strong stability case." Journal of Applied Probability 51, A (December 2014): 249–65. http://dx.doi.org/10.1239/jap/1417528479.

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We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional workload process. Tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, the presence of heavy tails totally changes these asymptotics. Here we focus on the case of strong stability where both nodes release fluid at sufficiently high speeds to minimise their mutual influence. We show that, as in the one-dimensional case, big jumps provide the main cause for workloads to become large, but now they can have multidimensional features. We first find the weak tail asymptotics of an arbitrary directional marginal of the stationary distribution at Poisson arrival epochs. In this analysis, decomposition formulae for the stationary distribution play a key role. Then we employ sample-path arguments to find the exact tail asymptotics of a directional marginal at renewal arrival epochs assuming one-dimensional batch arrivals.

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Foss, Sergey, and Masakiyo Miyazawa. "Two-node fluid network with a heavy-tailed random input: the strong stability case." Journal of Applied Probability 51, A (December 2014): 249–65. http://dx.doi.org/10.1017/s0021900200021318.

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We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional workload process. Tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, the presence of heavy tails totally changes these asymptotics. Here we focus on the case of strong stability where both nodes release fluid at sufficiently high speeds to minimise their mutual influence. We show that, as in the one-dimensional case, big jumps provide the main cause for workloads to become large, but now they can have multidimensional features. We first find the weak tail asymptotics of an arbitrary directional marginal of the stationary distribution at Poisson arrival epochs. In this analysis, decomposition formulae for the stationary distribution play a key role. Then we employ sample-path arguments to find the exact tail asymptotics of a directional marginal at renewal arrival epochs assuming one-dimensional batch arrivals.

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46

SERRANO, RAFAEL. "PORTFOLIO ALLOCATION IN A LEVY-TYPE JUMP-DIFFUSION MODEL WITH NONLIFE INSURANCE RISK." International Journal of Theoretical and Applied Finance 24, no. 01 (February 2021): 2150005. http://dx.doi.org/10.1142/s0219024921500059.

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We propose a model that integrates investment, underwriting, and consumption/dividend policy decisions for a nonlife insurer by using a risk control variable related to the wealth-income ratio of the firm. This facilitates the efficient transfer of insurance risk to capital markets since it allows to select simultaneously investments and underwriting volume. The model is particularly valuable for business lines with significant exposure to extreme events and disaster risk, as it accounts for features usually depicted during negative economic shocks and catastrophic events, such as Levy-type jump-diffusion dynamics for the financial log-returns that are in turn correlated with insurance premiums and liabilities, as well as worst-case scenarios in which policyholders in the insurance portfolio report claims with the same severity simultaneously. Using the martingale method, we determine an optimal solvency threshold or wealth-income ratio, and investment strategy that maximizes the expected utility from dividend payouts that follows a (possibly stochastic) consumption clock. We illustrate the main results with numerical examples for log- and power-utility functions, and (bounded variation) tempered stable Levy jumps.

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Zhang, Yingqi, Wei Cheng, Xiaowu Mu, and Caixia Liu. "Stochasticℋ∞Finite-Time Control of Discrete-Time Systems with Packet Loss." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/897481.

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This paper investigates the stochastic finite-time stabilization andℋ∞control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochasticℋ∞finite-time boundedness and then state feedback controllers are designed to guarantee stochasticℋ∞finite-time stabilization of the class of stochastic systems. The stochasticℋ∞finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.

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48

SHI, PENG. "Robust control of linear continuous time-delay systems with finite discrete jumps and norm-bounded uncertainties." International Journal of Systems Science 29, no. 12 (December 1998): 1381–92. http://dx.doi.org/10.1080/00207729808929624.

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Yang, Xiaojun, Zhengxin Weng, and Zuohua Tian. "On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps." Journal of Control Theory and Applications 2, no. 4 (November 2004): 411–15. http://dx.doi.org/10.1007/s11768-004-0049-z.

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TANIGUCHI, TAKESHI, and JIAOWAN LUO. "THE EXISTENCE AND ASYMPTOTIC BEHAVIOUR OF MILD SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS WITH INFINITE DELAYS DRIVEN BY POISSON JUMPS." Stochastics and Dynamics 09, no. 02 (June 2009): 217–29. http://dx.doi.org/10.1142/s0219493709002646.

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In this paper we consider a sufficient condition for mild solutions to exist and to be almost surely exponentially stable or exponentially ultimate bounded in mean square for the following stochastic evolution equation with infinite delays driven by Poisson jump processes: [Formula: see text] with an initial function X(s) = φ (s), -∞ < s ≤ 0, where φ : (-∞, 0] → H is a càdlàg function with [Formula: see text].

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Journal articles on the topic 'Bounded jumps'

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