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Journal articles on the topic 'Jump processes'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

Lee, Suzanne S., and Jan Hannig. "Detecting jumps from Lévy jump diffusion processes☆." Journal of Financial Economics 96, no. 2 (May 2010): 271–90. http://dx.doi.org/10.1016/j.jfineco.2009.12.009.

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2

V. Poliarus, O., Y. O. Poliakov, I. L. Nazarenko, Y. T. Borovyk, and M. V. Kondratiuk. "Detection of Jumps Parameters in Economic Processes(the Case of Modelling Profitability)." International Journal of Engineering & Technology 7, no. 4.3 (September 15, 2018): 488. http://dx.doi.org/10.14419/ijet.v7i4.3.19922.

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A new method of parameters jumps detection in economic processes is presented. A jump of the economic process parameter must be understood as a rapid parameter change for a time that does not exceed the period of process registration. A system of stochastic differential equations for a posteriori density probability of a jump is synthesized. The solution of the system is the probability of a parameter jump, the estimation and variance of the jump in the presence of a priori information under conditions of noise influence. The simulation results are conducted for profitability of machine building industry of Kharkiv region, Ukraine. The system provides detection of jump parameters, even in conditions of intense noise of economic nature. To increase the probability of finding jumps it is necessary to have a priori information.

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3

Breuer, Lothar. "A quintuple law for Markov additive processes with phase-type jumps." Journal of Applied Probability 47, no. 2 (June 2010): 441–58. http://dx.doi.org/10.1239/jap/1276784902.

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We consider a Markov additive process (MAP) with phase-type jumps, starting at 0. Given a positive level u, we determine the joint distribution of the undershoot and overshoot of the first jump over the level u, the maximal level before this jump, the time of attaining this maximum, and the time between the maximum and the jump. The analysis is based on first passage times and time reversion of MAPs. A marginal of the derived distribution is the Gerber-Shiu function, which is of interest to insurance risk. Several examples serve to compare the present result with the literature.

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4

Breuer, Lothar. "A quintuple law for Markov additive processes with phase-type jumps." Journal of Applied Probability 47, no. 02 (June 2010): 441–58. http://dx.doi.org/10.1017/s0021900200006744.

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We consider a Markov additive process (MAP) with phase-type jumps, starting at 0. Given a positive level u, we determine the joint distribution of the undershoot and overshoot of the first jump over the level u, the maximal level before this jump, the time of attaining this maximum, and the time between the maximum and the jump. The analysis is based on first passage times and time reversion of MAPs. A marginal of the derived distribution is the Gerber-Shiu function, which is of interest to insurance risk. Several examples serve to compare the present result with the literature.

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5

Ratanov, Nikita. "Damped jump-telegraph processes." Statistics & Probability Letters 83, no. 10 (October 2013): 2282–90. http://dx.doi.org/10.1016/j.spl.2013.06.018.

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6

Mufa, Chen. "Coupling for jump processes." Acta Mathematica Sinica 2, no. 2 (June 1986): 123–36. http://dx.doi.org/10.1007/bf02564874.

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7

Gyöngy, István, and Sizhou Wu. "On Itô formulas for jump processes." Queueing Systems 98, no. 3-4 (August 2021): 247–73. http://dx.doi.org/10.1007/s11134-021-09709-8.

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AbstractA well-known Itô formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical Itô formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite-dimensional Itô formula for continuous semimartingales from Krylov (Probab Theory Relat Fields 147:583–605, 2010) to a class of $$L_p$$ L p -valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.

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8

Wang, Guanying, Xingchun Wang, and Zhongyi Liu. "PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES." Probability in the Engineering and Informational Sciences 31, no. 2 (December 14, 2016): 121–38. http://dx.doi.org/10.1017/s0269964816000486.

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This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

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9

Dumitrescu, Monica E. "Some informational properties of Markov pure-jump processes." Časopis pro pěstování matematiky 113, no. 4 (1988): 429–34. http://dx.doi.org/10.21136/cpm.1988.118348.

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10

Fuchs, Philip X., Julia Mitteregger, Dominik Hoelbling, Hans-Joachim K. Menzel, Jeffrey W. Bell, Serge P. von Duvillard, and Herbert Wagner. "Relationship between General Jump Types and Spike Jump Performance in Elite Female and Male Volleyball Players." Applied Sciences 11, no. 3 (January 25, 2021): 1105. http://dx.doi.org/10.3390/app11031105.

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In performance testing, it is well-established that general jump types like squat and countermovement jumps have great reliability, but the relationship with volleyball spike jumps is unclear. The objectives of this study were to analyze the relationship between general and spike jumps and to provide improved models for predicting spike jump height by general jump performance. Thirty female and male elite volleyball players performed general and spike jumps in a randomized order. Two AMTI force plates (2000 Hz) and 13 Vicon MX cameras (250 Hz) captured kinematic and kinetic data. Correlation and stepwise-forward regression analyses were conducted at p < 0.05. Simple regression models with general jump height as the only predictor for spike jumps revealed 0.52 ≤ R2 ≤ 0.76 for all general jumps in both sexes (p < 0.05). Alternative models including rate of force development and impulse improved predictions during squat jumps from R2 = 0.76 to R2 = 0.92 (p < 0.05) in females and from R2 = 0.61 to R2 = 0.71 (p < 0.05) in males, and during countermovement jumps with arm swing from R2 = 0.52 to R2 = 0.78 (p < 0.01) in males. The findings include improved prediction models for spike jump height based on general jump performance. The derived formulas can be applied in general jump testing to improve the assessment of sport-specific spike jump performance.

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11

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 4 (December 2010): 1147–71. http://dx.doi.org/10.1239/aap/1293113155.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

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12

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 04 (December 2010): 1147–71. http://dx.doi.org/10.1017/s0001867800004560.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

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13

Schultz, Christopher J., Lawrence D. Carey, Elise V. Schultz, and Richard J. Blakeslee. "Insight into the Kinematic and Microphysical Processes that Control Lightning Jumps." Weather and Forecasting 30, no. 6 (November 19, 2015): 1591–621. http://dx.doi.org/10.1175/waf-d-14-00147.1.

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Abstract A detailed case study analysis of four thunderstorms is performed using polarimetric and multi-Doppler capabilities to provide specificity on the physical and dynamical drivers behind lightning jumps. The main differences between small increases in the total flash rate and a lightning jump are the increases in graupel mass and updraft volumes ≥10 m s−1 between the −10° and −40°C isotherms. Updraft volumes ≥10 m s−1 increased in magnitude at least 3–5 min in advance of the increase in both graupel mass and total flash rate. Updraft volumes ≥10 m s−1 are more robustly correlated to total flash rate than maximum updraft speed over a thunderstorm’s entire life cycle. However, peak updraft speeds increase prior to 8 of the 12 lightning jumps examined. Decreases in mean and median flash footprint size during increases in total lightning are observed in all four thunderstorms and are most notable during development stages within the most intense storms. However, this inverse relationship breaks down on larger storm scales as storms mature and anvils and stratiform regions developed with time. Promisingly, smaller flash sizes are still collocated with the strongest updraft speeds, while larger flash sizes are observed within weaker updraft regions. The results herein emphasize the following for lightning jump applications: both the lightning jump sigma level and the resultant magnitude of the total flash rate must be employed in conjunction to assess storm intensity using lightning data. The sigma-level magnitude of the lightning jump is the early warning that indicates that rapid intensification is occurring, while the magnitude of the total flash rate provides insight into the size and maintenance of the updraft volume and graupel mass. These cases serve as conceptual models for future applications of the lightning jump algorithm for hazardous weather monitoring.

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14

D’Onofrio, Giuseppe, and Alessandro Lanteri. "Approximating the First Passage Time Density of Diffusion Processes with State-Dependent Jumps." Fractal and Fractional 7, no. 1 (December 28, 2022): 30. http://dx.doi.org/10.3390/fractalfract7010030.

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We study the problem of the first passage time through a constant boundary for a jump diffusion process whose infinitesimal generator is a nonlocal Jacobi operator. Due to the lack of analytical results, we address the problem using a discretization scheme for simulating the trajectories of jump diffusion processes with state-dependent jumps in both frequency and amplitude. We obtain numerical approximations on their first passage time probability density functions and results for the qualitative behavior of other statistics of this random variable. Finally, we provide two examples of application of the method for different choices of the distribution involved in the mechanism of generation of the jumps.

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15

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 1 (March 2000): 140–58. http://dx.doi.org/10.1239/aap/1013540027.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.

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16

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 01 (March 2000): 140–58. http://dx.doi.org/10.1017/s0001867800009812.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.

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17

Liu, Shican, Yanli Zhou, Yonghong Wu, and Xiangyu Ge. "Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes." Journal of Function Spaces 2019 (February 3, 2019): 1–12. http://dx.doi.org/10.1155/2019/9754679.

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In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

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18

MINA, KARL FRIEDRICH, GERALD H. L. CHEANG, and CARL CHIARELLA. "APPROXIMATE HEDGING OF OPTIONS UNDER JUMP-DIFFUSION PROCESSES." International Journal of Theoretical and Applied Finance 18, no. 04 (June 2015): 1550024. http://dx.doi.org/10.1142/s0219024915500247.

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We consider the problem of hedging a European-type option in a market where asset prices have jump-diffusion dynamics. It is known that markets with jumps are incomplete and that there are several risk-neutral measures one can use to price and hedge options. In order to address these issues, we approximate such a market by discretizing the jumps in an averaged sense, and complete it by including traded options in the model and hedge portfolio. Under suitable conditions, we get a unique risk-neutral measure, which is used to determine the option price integro-partial differential equation, along with the asset positions that will replicate the option payoff. Upon implementation on a particular set of stock and option prices, our approximate complete market hedge yields easily computable asset positions that equal those of the minimal variance hedge, while at the same time offers protection against upward jumps and higher profit compared to delta hedging.

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19

Borovkov, K., and G. Last. "On level crossings for a general class of piecewise-deterministic Markov processes." Advances in Applied Probability 40, no. 03 (September 2008): 815–34. http://dx.doi.org/10.1017/s0001867800002809.

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We consider a piecewise-deterministic Markov process (Xt) governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. The paper deals with the point processof upcrossings of some levelbby (Xt). We prove a version of Rice's formula relating the stationary density of (Xt) to level crossing intensities and show that, for a wide class of processes (Xt), asb→ ∞, the scaled point processwhere ν+(b) denotes the intensity of upcrossings ofb, converges weakly to a geometrically compound Poisson process.

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20

Flynn, C. P. "Atomic Jump Processes in Crystals." Materials Science Forum 15-18 (January 1987): 281–300. http://dx.doi.org/10.4028/www.scientific.net/msf.15-18.281.

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21

Schilling, Rene L. "Financial Modelling with Jump Processes." Journal of the Royal Statistical Society: Series A (Statistics in Society) 168, no. 1 (January 2005): 250–51. http://dx.doi.org/10.1111/j.1467-985x.2004.00347_3.x.

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22

Bingham, N. H. "Financial Modelling With Jump Processes." Journal of the American Statistical Association 101, no. 475 (September 2006): 1315–16. http://dx.doi.org/10.1198/jasa.2006.s130.

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23

Treloar, Katrina K., Matthew J. Simpson, and Scott W. McCue. "Velocity-jump processes with proliferation." Journal of Physics A: Mathematical and Theoretical 46, no. 1 (December 5, 2012): 015003. http://dx.doi.org/10.1088/1751-8113/46/1/015003.

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24

Yang, Xiaochuan. "Multifractality of jump diffusion processes." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, no. 4 (November 2018): 2042–74. http://dx.doi.org/10.1214/17-aihp864.

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25

Ceci, Claudia, and Anna Gerardi. "Controlled partially observed jump processes." Nonlinear Analysis: Theory, Methods & Applications 47, no. 4 (August 2001): 2449–60. http://dx.doi.org/10.1016/s0362-546x(01)00368-6.

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26

Antczak, Grazyna, and Gert Ehrlich. "Jump processes in surface diffusion." Surface Science Reports 62, no. 2 (February 2007): 39–61. http://dx.doi.org/10.1016/j.surfrep.2006.12.001.

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27

Simon, Thomas. "Support theorem for jump processes." Stochastic Processes and their Applications 89, no. 1 (September 2000): 1–30. http://dx.doi.org/10.1016/s0304-4149(00)00008-9.

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28

Conforti, Giovanni, Paolo Dai Pra, and Sylvie Rœlly. "Reciprocal Class of Jump Processes." Journal of Theoretical Probability 30, no. 2 (November 24, 2015): 551–80. http://dx.doi.org/10.1007/s10959-015-0655-3.

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29

Luo, Jiaowan. "Doubly perturbed jump-diffusion processes." Journal of Mathematical Analysis and Applications 351, no. 1 (March 2009): 147–51. http://dx.doi.org/10.1016/j.jmaa.2008.09.024.

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30

Bueno-Guerrero, Alberto, and Steven P. Clark. "Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps." Mathematics 12, no. 1 (December 26, 2023): 82. http://dx.doi.org/10.3390/math12010082.

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We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes.

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31

Lefebvre, Mario. "First-Passage Times and Optimal Control of Integrated Jump-Diffusion Processes." Fractal and Fractional 7, no. 2 (February 3, 2023): 152. http://dx.doi.org/10.3390/fractalfract7020152.

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Let Y(t) be a one-dimensional jump-diffusion process and X(t) be defined by dX(t)=ρ[X(t),Y(t)]dt, where ρ(·,·) is either a strictly positive or negative function. First-passage-time problems for the degenerate two-dimensional process (X(t),Y(t)) are considered in the case when the process leaves the continuation region at the latest at the moment of the first jump, and the problem of optimally controlling the process is treated as well. A particular problem, in which ρ[X(t),Y(t)]=Y(t)−X(t) and Y(t) is a standard Brownian motion with jumps, is solved explicitly.

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32

Borovkov, K., and G. Last. "On level crossings for a general class of piecewise-deterministic Markov processes." Advances in Applied Probability 40, no. 3 (September 2008): 815–34. http://dx.doi.org/10.1239/aap/1222868187.

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We consider a piecewise-deterministic Markov process (Xt) governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. The paper deals with the point process of upcrossings of some level b by (Xt). We prove a version of Rice's formula relating the stationary density of (Xt) to level crossing intensities and show that, for a wide class of processes (Xt), as b → ∞, the scaled point process where ν+(b) denotes the intensity of upcrossings of b, converges weakly to a geometrically compound Poisson process.

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33

Duan, Jin-Chuan, Peter Ritchken, and Zhiqiang Sun. "APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICING." Mathematical Finance 16, no. 1 (January 2006): 21–52. http://dx.doi.org/10.1111/j.1467-9965.2006.00259.x.

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34

Miles, Christopher E., and James P. Keener. "Jump locations of jump-diffusion processes with state-dependent rates." Journal of Physics A: Mathematical and Theoretical 50, no. 42 (September 22, 2017): 425003. http://dx.doi.org/10.1088/1751-8121/aa8a90.

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35

Boucherie, Richard J., and Nico M. Van Dijk. "Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes." Advances in Applied Probability 22, no. 2 (June 1990): 433–55. http://dx.doi.org/10.2307/1427544.

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Reversible spatial birth-death processes are studied with simultaneous jumps of multi-components. A relationship is established between (i) a product-form solution, (ii) a partial symmetry condition on the jump rates and (iii) a solution of a deterministic concentration equation. Applications studied are reversible networks of queues with batch services and blocking and clustering processes such as those found in polymerization chemistry. As illustrated by examples, known results are hereby unified and extended. An expectation interpretation of the transition rates is included.

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36

Boucherie, Richard J., and Nico M. Van Dijk. "Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes." Advances in Applied Probability 22, no. 02 (June 1990): 433–55. http://dx.doi.org/10.1017/s0001867800019650.

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Reversible spatial birth-death processes are studied with simultaneous jumps of multi-components. A relationship is established between (i) a product-form solution, (ii) a partial symmetry condition on the jump rates and (iii) a solution of a deterministic concentration equation. Applications studied are reversible networks of queues with batch services and blocking and clustering processes such as those found in polymerization chemistry. As illustrated by examples, known results are hereby unified and extended. An expectation interpretation of the transition rates is included.

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37

Pfeifer, Dietmar, and Ursula Heller. "A martingale characterization of mixed Poisson processes." Journal of Applied Probability 24, no. 1 (March 1987): 246–51. http://dx.doi.org/10.2307/3214076.

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It is shown that an elementary pure birth process is a mixed Poisson process iff the sequence of post-jump intensities forms a martingale with respect to the σ -fields generated by the jump times of the process. In this case, the post-jump intensities converge almost surely to the mixing random variable of the process.

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38

Pfeifer, Dietmar, and Ursula Heller. "A martingale characterization of mixed Poisson processes." Journal of Applied Probability 24, no. 01 (March 1987): 246–51. http://dx.doi.org/10.1017/s0021900200030783.

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It is shown that an elementary pure birth process is a mixed Poisson process iff the sequence of post-jump intensities forms a martingale with respect to the σ -fields generated by the jump times of the process. In this case, the post-jump intensities converge almost surely to the mixing random variable of the process.

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39

Amorino, Chiara, and Eulalia Nualart. "Optimal convergence rates for the invariant density estimation of jump-diffusion processes." ESAIM: Probability and Statistics 26 (2022): 126–51. http://dx.doi.org/10.1051/ps/2022001.

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We aim at estimating the invariant density associated to a stochastic differential equation with jumps in low dimension, which is for d = 1 and d = 2. We consider a class of fully non-linear jump diffusion processes whose invariant density belongs to some Hölder space. Firstly, in dimension one, we show that the kernel density estimator achieves the convergence rate 1/T, which is the optimal rate in the absence of jumps. This improves the convergence rate obtained in Amorino and Gloter [J. Stat. Plann. Inference 213 (2021) 106–129], which depends on the Blumenthal-Getoor index for d = 1 and is equal to (logT)/T for d = 2. Secondly, when the jump and diffusion coefficients are constant and the jumps are finite, we show that is not possible to find an estimator with faster rates of estimation. Indeed, we get some lower bounds with the same rates {1/T, (logT)/T} in the mono and bi-dimensional cases, respectively. Finally, we obtain the asymptotic normality of the estimator in the one-dimensional case for the fully non-linear process.

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40

Ribeiro, M. Teresa S., Filipe Conceição, and Matheus M. Pacheco. "Proficiency Barrier in Track and Field: Adaptation and Generalization Processes." Sensors 24, no. 3 (February 4, 2024): 1000. http://dx.doi.org/10.3390/s24031000.

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The literature on motor development and training assumes a hierarchy for learning skills—learning the “fundamentals”—that has yet to be empirically demonstrated. The present study addressed this issue by verifying (1) whether this strong hierarchy (i.e., the proficiency barrier) holds between three fundamental skills and three sport skills and (2) considering different transfer processes (generalization/adaptation) that would occur as a result of the existence of this strong hierarchy. Twenty-seven children/adolescents participated in performing the countermovement jump, standing long jump, leap, high jump, long jump, and hurdle transposition. We identified the proficiency barrier in two pairs of tasks (between the countermovement jump and high jump and between the standing long jump and long jump). Nonetheless, the transfer processes were not related to the proficiency barrier. We conclude that the proposed learning hierarchy holds for some tasks. The underlying reason for this is still unknown.

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41

Chow, Gary Chi-Ching, Yu-Hin Kong, and Wai-Yan Pun. "The Concurrent Validity and Test-Retest Reliability of Possible Remote Assessments for Measuring Countermovement Jump: My Jump 2, HomeCourt & Takei Vertical Jump Meter." Applied Sciences 13, no. 4 (February 7, 2023): 2142. http://dx.doi.org/10.3390/app13042142.

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Mobile applications and portable assessments make remote self-assessment of the countermovement jump (CMJ) test possible. This study aimed to investigate the concurrent validity and test–retest reliability of three portable measurement systems for CMJ. Thirty physically active college students visited the laboratory twice, with two days in between, and performed three jumps each day. All jumps were recorded by My Jump 2, HomeCourt, and the Takei Vertical Jump Meter (TVJM) simultaneously. Results indicated significant differences among the three systems (p < 0.01). HomeCourt tended to present the highest jump height mean value (46.10 ± 7.57 cm) compared with TVJM (42.02 ± 8.11 cm) and My Jump 2 (40.85 ± 7.86 cm). High concurrent validities among assessments were found (r = 0.85–0.93). Good to excellent reliability of jump assessments was demonstrated (ICC3,1 = 0.80–0.96). Reliable coefficients of variation were shown in all measurements (2.58–5.92%). Significant differences were revealed among the three apparatuses while they demonstrated high intra-device test–retest reliability. TVJM was the most reliable, and average jump heights were recommended for analysis.

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42

Huzak, Miljenko, Mihael Perman, Hrvoje Šikić, and Zoran Vondraček. "Ruin probabilities for competing claim processes." Journal of Applied Probability 41, no. 3 (September 2004): 679–90. http://dx.doi.org/10.1239/jap/1091543418.

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LetC1,C2,…,Cmbe independent subordinators with finite expectations and denote their sum byC. Consider the classical risk processX(t) =x+ct-C(t). The ruin probability is given by the well-known Pollaczek–Khinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinatorsCi. Formulae for the probability that ruin is caused byCiare derived. These formulae can be extended to perturbed risk processes of the typeX(t) =x+ct-C(t) +Z(t), whereZis a Lévy process with mean 0 and no positive jumps.

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43

Serfozo, Richard F. "Reversible Markov processes on general spaces and spatial migration processes." Advances in Applied Probability 37, no. 3 (September 2005): 801–18. http://dx.doi.org/10.1239/aap/1127483748.

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In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

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Serfozo, Richard F. "Reversible Markov processes on general spaces and spatial migration processes." Advances in Applied Probability 37, no. 03 (September 2005): 801–18. http://dx.doi.org/10.1017/s0001867800000483.

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In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

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45

Shimizu, Yasutaka. "Threshold selection in jump-discriminant filter for discretely observed jump processes." Statistical Methods & Applications 19, no. 3 (April 8, 2010): 355–78. http://dx.doi.org/10.1007/s10260-010-0134-z.

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46

Duong, Dam Ton, and Phung Ngoc Nguyen. "Stochastic differential of Ito – Levy processes." Science and Technology Development Journal 19, no. 2 (June 30, 2016): 80–83. http://dx.doi.org/10.32508/stdj.v19i2.792.

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In this paper, we continue to expand some results to get the product rule for differential of stochastic processes with jump, and apply for some special processes like pure jump process, Levy-Ornstein-Uhlenbeck process, geometric Levy process, in models of finance, ecomomics, and information technology.

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Carpinteyro, Martha, Francisco Venegas-Martínez, and Alí Aali-Bujari. "Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility." Mathematics 9, no. 4 (February 19, 2021): 407. http://dx.doi.org/10.3390/math9040407.

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This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by fractional Brownian motions, combined with Poisson processes and modulated by continuous-time homogeneous Markov chains. The calibration is carried out by estimating the Jump Generalized Autoregressive Conditional Heteroscedasticity (Jump-GARCH) and Markov regime-switching models of each precious metal, as well as computing their Hurst exponents. The novelty in this research is the use of non-linear, non-normal, multi-factor, time-varying risk stochastic models, useful for an investors’ decision-making process when they intend to include precious metals in their portfolios as safe-haven assets. The main empirical results are as follows: (1) all metals stay in low volatility most of the time and have long memories, which means that past returns have an effect on current and future returns; (2) silver and platinum have the largest jump sizes; (3) silver’s negative jumps have the highest intensity; and (4) silver reacts more than gold and platinum, and it is also the most volatile, having the highest probability of intensive jumps. Gold is the least volatile, as its percentage of jumps is the lowest and the intensity of its jumps is lower than that of the other two metals. Finally, a set of recommendations is provided for the decision-making process of an average investor looking to buy and sell precious metals.

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Kohatsu-Higa, Arturo, Eulalia Nualart, and Ngoc Khue Tran. "Density estimates for jump diffusion processes." Applied Mathematics and Computation 420 (May 2022): 126814. http://dx.doi.org/10.1016/j.amc.2021.126814.

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Cheng, Hui-Hui, and Yong-Hua Mao. "Polynomial convergence for reversible jump processes." Statistics & Probability Letters 173 (June 2021): 109081. http://dx.doi.org/10.1016/j.spl.2021.109081.

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Sworder, D. D., and J. E. Boyd. "Jump-diffusion processes in tracking/recognition." IEEE Transactions on Signal Processing 46, no. 1 (1998): 235–39. http://dx.doi.org/10.1109/78.651226.

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