Статті в журналах: "Exact asymptotics"

1

Di Francesco, P., O. Golinelli, and E. Guitter. "Meanders: exact asymptotics." Nuclear Physics B 570, no. 3 (March 2000): 699–712. http://dx.doi.org/10.1016/s0550-3213(99)00753-1.

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2

Es-Saghouani, A., and M. Mandjes. "Exact multivariate workload asymptotics." Mathematical Methods of Operations Research 78, no. 3 (August 20, 2013): 405–15. http://dx.doi.org/10.1007/s00186-013-0450-9.

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3

Foley, Robert D., and David R. McDonald. "Bridges and networks: Exact asymptotics." Annals of Applied Probability 15, no. 1B (February 2005): 542–86. http://dx.doi.org/10.1214/105051604000000675.

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4

Kuzmina, Liudmila, and Yuri Osipov. "DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM." International Journal for Computational Civil and Structural Engineering 16, no. 4 (December 28, 2020): 50–56. http://dx.doi.org/10.22337/2587-9618-2020-16-4-50-56.

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Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution

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5

Tsapenko, Nikolai Evgenievich. "Riccatis Equation. Asymptotics of Exact Solution." International Journal of Mathematical Research 5, no. 1 (2016): 25–39. http://dx.doi.org/10.18488/journal.24/2016.5.1/24.1.25.39.

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6

Braaksma, B. L. J., G. K. Immink, and Y. Sibuya. "The Stokes phenomenon in exact asymptotics." Pacific Journal of Mathematics 187, no. 1 (January 1, 1999): 13–51. http://dx.doi.org/10.2140/pjm.1999.187.13.

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7

Joyce, G. S., E. R. Pike, and S. Sarkar. "Exact asymptotics for the laser linewidth." Journal of Physics A: Mathematical and General 27, no. 15 (August 7, 1994): 5265–71. http://dx.doi.org/10.1088/0305-4470/27/15/024.

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8

Di Francesco, P., E. Guitter, and J. L. Jacobsen. "Exact meander asymptotics: a numerical check." Nuclear Physics B 580, no. 3 (August 2000): 757–95. http://dx.doi.org/10.1016/s0550-3213(00)00273-x.

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9

Wu, Ten-Ming, David W. Brown, and Katja Lindenberg. "Exact asymptotics for dissipative quantum tunneling." Chemical Physics 146, no. 3 (October 1990): 445–51. http://dx.doi.org/10.1016/0301-0104(90)80063-4.

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10

Kurina, Galina, and Margarita Kalashnikova. "Justification of Direct Scheme for Asymptotic Solving Three-Tempo Linear-Quadratic Control Problems under Weak Nonlinear Perturbations." Axioms 11, no. 11 (November 16, 2022): 647. http://dx.doi.org/10.3390/axioms11110647.

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The paper deals with an application of the direct scheme method, consisting of immediately substituting a postulated asymptotic solution into a problem condition and determining a series of control problems for finding asymptotics terms, for asymptotics construction of a solution of a weakly nonlinearly perturbed linear-quadratic optimal control problem with three-tempo state variables. For the first time, explicit formulas for linear-quadratic optimal control problems, from which all terms of the asymptotic expansion are found, are justified, and the estimates of the proximity between the asymptotic and exact solutions are proved for the control, state trajectory, and minimized functional. Non-increasing of the minimized functional, if a next approximation to the optimal control is used, following from the proposed algorithm of the asymptotics construction, is also established.

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11

Dębicki, Krzysztof, Enkelejd Hashorva, and Lanpeng Ji. "Parisian ruin of self-similar Gaussian risk processes." Journal of Applied Probability 52, no. 3 (September 2015): 688–702. http://dx.doi.org/10.1239/jap/1445543840.

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In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.

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12

Dębicki, Krzysztof, Enkelejd Hashorva, and Lanpeng Ji. "Parisian ruin of self-similar Gaussian risk processes." Journal of Applied Probability 52, no. 03 (September 2015): 688–702. http://dx.doi.org/10.1017/s0021900200113373.

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In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.

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13

Strichartz, Robert S. "Exact spectral asymptotics on the Sierpinski gasket." Proceedings of the American Mathematical Society 140, no. 5 (May 1, 2012): 1749–55. http://dx.doi.org/10.1090/s0002-9939-2011-11309-1.

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14

Gelfand, A. E., and D. K. Dey. "Bayesian Model Choice: Asymptotics and Exact Calculations." Journal of the Royal Statistical Society: Series B (Methodological) 56, no. 3 (September 1994): 501–14. http://dx.doi.org/10.1111/j.2517-6161.1994.tb01996.x.

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15

Hashorva, Enkelejd. "Exact tail asymptotics of aggregated parametrised risk." Journal of Mathematical Analysis and Applications 400, no. 1 (April 2013): 187–99. http://dx.doi.org/10.1016/j.jmaa.2012.11.047.

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16

Pirjol, Dan, and Lingjiong Zhu. "SHORT MATURITY ASIAN OPTIONS FOR THE CEV MODEL." Probability in the Engineering and Informational Sciences 33, no. 2 (June 5, 2018): 258–90. http://dx.doi.org/10.1017/s0269964818000165.

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We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the constant elasticity of variance (CEV) model. The leading order short maturity limit of the Asian option prices under the CEV model is obtained in closed form. We propose an analytical approximation for the Asian options prices which reproduces the exact short maturity asymptotics, and demonstrate good numerical agreement of the asymptotic results with Monte Carlo simulations and benchmark test cases for option parameters relevant for practical applications.

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17

Chapling, Richard. "Asymptotics of certain sums required in loop regularisation." Modern Physics Letters A 31, no. 04 (January 26, 2016): 1650030. http://dx.doi.org/10.1142/s0217732316500309.

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We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to the form of the regularised integrals used in loop regularisation. We show all three are true, extend them to more general powers and produce their full asymptotic series. We also extend a classical result to produce an exact formula for the sum in the last.

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18

Tsitsiashvili, G. S. "Moments of Random Allocation Processes Reaching a Boundary." Journal of Applied Probability 44, no. 4 (December 2007): 990–95. http://dx.doi.org/10.1239/jap/1197908819.

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In this paper we develop some results presented by Gani (2004), deriving moments for random allocation processes. These moments correspond to the allocation processes reaching some domain boundary. Exact formulae for means, variances, and probability generating functions as well as some asymptotic formulae for moments of random allocation processes are obtained. A special choice of the asymptotics and of the domain allows us to reduce a complicated numerical procedure to a simple asymptotic one.

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19

Tsitsiashvili, G. S. "Moments of Random Allocation Processes Reaching a Boundary." Journal of Applied Probability 44, no. 04 (December 2007): 990–95. http://dx.doi.org/10.1017/s0021900200003685.

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In this paper we develop some results presented by Gani (2004), deriving moments for random allocation processes. These moments correspond to the allocation processes reaching some domain boundary. Exact formulae for means, variances, and probability generating functions as well as some asymptotic formulae for moments of random allocation processes are obtained. A special choice of the asymptotics and of the domain allows us to reduce a complicated numerical procedure to a simple asymptotic one.

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20

FRIDMAN, G. M. "Matched asymptotics for two-dimensional planing hydrofoils with spoilers." Journal of Fluid Mechanics 358 (March 10, 1998): 259–81. http://dx.doi.org/10.1017/s0022112097008215.

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The purpose of the paper is to demonstrate the effectiveness of the matched asymptotic expansions (MAE) method for the planing flow problem. The matched asymptotics, taking into account the flow nonlinearities in those regions where they are most pronounced (i.e. in the vicinity of the edges), are shown to significantly extend the range where the linear theory gives good results. Two model problems are used: the planing flat plate with a spoiler on the trailing edge and the curved planing foil. Asymptotic solutions obtained by the MAE method are compared with those obtained using linear and exact nonlinear theories. Based on the results, the asymptotic solution to the planing problem under the gravity is proposed.

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21

DiblÍk, Josef, and Rigoberto Medina. "Exact asymptotics of positive solutions to Dickman equation." Discrete & Continuous Dynamical Systems - B 23, no. 1 (2018): 101–21. http://dx.doi.org/10.3934/dcdsb.2018007.

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22

Nikitin, Ya Yu, and R. S. Pusev. "Exact Small Deviation Asymptotics for Some Brownian Functionals." Theory of Probability & Its Applications 57, no. 1 (January 2013): 60–81. http://dx.doi.org/10.1137/s0040585x97985790.

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23

Dȩbicki, Krzysztof, Enkelejd Hashorva, Lanpeng Ji, and Kamil Tabiś. "Extremes of vector-valued Gaussian processes: Exact asymptotics." Stochastic Processes and their Applications 125, no. 11 (November 2015): 4039–65. http://dx.doi.org/10.1016/j.spa.2015.05.015.

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24

Foley, R. D., and D. R. McDonald. "Join the shortest queue: stability and exact asymptotics." Annals of Applied Probability 11, no. 3 (August 2001): 569–607. http://dx.doi.org/10.1214/aoap/1015345342.

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25

Hashorva, Enkelejd. "Exact tail asymptotics in bivariate scale mixture models." Extremes 15, no. 1 (March 11, 2011): 109–28. http://dx.doi.org/10.1007/s10687-011-0129-7.

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26

Miyoshi, Naoto, and Tomoyuki Shirai. "Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models." Probability and Mathematical Statistics 37, no. 2 (May 14, 2018): 431–53. http://dx.doi.org/10.19195/0208-4147.37.2.12.

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TAIL ASYMPTOTICS OF SIGNAL-TO-INTERFERENCE RATI ODISTRIBUTION IN SPATIAL CELLULAR NETWORK MODELSWe consider a spatial stochastic model of wireless cellular networks, where the base stations BSs are deployed according to a simple and stationary point process on Rd, d > 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio SIR, which is a key quantity in wireless communications. In the case where the pathloss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and -Ginibrebased models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.

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27

Kuzmina, Liudmila, Yuri Osipov, and Yulia Zheglova. "Global asymptotics of filtration in porous media." E3S Web of Conferences 97 (2019): 05002. http://dx.doi.org/10.1051/e3sconf/20199705002.

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Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The aim of the study is to construct an explicit analytical solution of the filtration problem. A one-dimensional model of deep bed filtration of a monodisperse suspension in a homogeneous porous medium with size-exclusion mechanism of particles retention is considered. Solid particles are freely transferred by the carrier fluid through large pores and get stuck in the throats of small pores. The mathematical model of deep bed filtration includes the mass balance equation for suspended and retained particles and the kinetic equation for the deposit growth. The model describes the movement of concentrations front of suspended and retained particles in an empty porous medium. Behind the concentrations front, solid particles are transported by a carrier fluid, accompanied by the formation of a deposit. The complex model has no explicit exact solution. To construct the asymptotic solution in explicit form, methods of nonlinear asymptotic analysis are used. The new coordinate transformation allows to obtain a parameter that is small at all points of the porous sample at any time. In this paper, a global asymptotic solution of the filtration problem is constructed using a new small parameter. Numerical calculations are performed for a nonlinear filtration coefficient found experimentally. Calculations confirm the closeness of the asymptotics to the solution in the entire filtration domain. For a nonlinear filtration coefficient, the asymptotics is closer to the numerical solution than the exact solution of the problem with a linear coefficient. The analytical solution obtained in the paper can be used to analyze solutions of problems of underground fluid mechanics and fine-tune laboratory experiments.

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28

Korostelev, A. P., and V. G. Spokoiny. "Exact Asymptotics of Minimax Bahadur Risk in Lipschitz Regression." Statistics 28, no. 1 (January 1996): 13–24. http://dx.doi.org/10.1080/02331889708802544.

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29

Garoni, T. M., and N. E. Frankel. "Lévy flights: Exact results and asymptotics beyond all orders." Journal of Mathematical Physics 43, no. 5 (2002): 2670. http://dx.doi.org/10.1063/1.1467095.

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30

Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 3 (September 2003): 704–20. http://dx.doi.org/10.1239/jap/1059060897.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

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31

Sharpnack, James, and Ery Arias-Castro. "Exact asymptotics for the scan statistic and fast alternatives." Electronic Journal of Statistics 10, no. 2 (2016): 2641–84. http://dx.doi.org/10.1214/16-ejs1188.

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32

Chigansky, Pavel, and Marina Kleptsyna. "Exact asymptotics in eigenproblems for fractional Brownian covariance operators." Stochastic Processes and their Applications 128, no. 6 (June 2018): 2007–59. http://dx.doi.org/10.1016/j.spa.2017.08.019.

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33

Richards, Donald St P. "Exact Asymptotics for some Probability Distributions on Compact Manifolds." Annals of Statistics 23, no. 5 (October 1995): 1582–86. http://dx.doi.org/10.1214/aos/1176324313.

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34

Kuhn, Julia, Michel Mandjes, and Thomas Taimre. "EXACT ASYMPTOTICS OF SAMPLE-MEAN-RELATED RARE-EVENT PROBABILITIES." Probability in the Engineering and Informational Sciences 32, no. 2 (January 16, 2017): 207–28. http://dx.doi.org/10.1017/s0269964816000541.

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Relying only on the classical Bahadur–Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (asn→∞) of$$ {\open P}\left({\max_{i\in\{1,\ldots,d_x\}}\bar X_{i,n} \les \min_{i\in\{1,\ldots,d_y\}}\bar Y_{i,n}}\right),$$with the${\bar X}_{i,n}{\rm s}$(${\bar Y}_{i,n}{\rm s}$, respectively) denotingdx(dy) independent copies of sample means associated with the random variableX(Y). Assuming${\open E}X \gt {\open E}Y$, this is a rare event probability that vanishes essentially exponentially, but with an additional polynomial term. We also point out how the probability of interest can be estimated using importance sampling in a logarithmically efficient way. To demonstrate the usefulness of the result, we show how it can be applied to compare the order statistics of the sample means of the two populations. This has various applications, for instance in queuing or packing problems.

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35

Dębicki, Krzysztof, and Michel Mandjes. "Exact overflow asymptotics for queues with many Gaussian inputs." Journal of Applied Probability 40, no. 03 (September 2003): 704–20. http://dx.doi.org/10.1017/s0021900200019653.

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In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

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36

Petrova, Yu P. "Exact L2-Small Ball Asymptotics for Some Durbin Processes." Journal of Mathematical Sciences 244, no. 5 (January 9, 2020): 842–57. http://dx.doi.org/10.1007/s10958-020-04657-9.

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37

Spătaru, A. "Exact Asymptotics in log log Laws for Random Fields." Journal of Theoretical Probability 17, no. 4 (October 2004): 943–65. http://dx.doi.org/10.1007/s10959-004-0584-z.

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38

Bennett, T., C. J. Howls, G. Nemes, and A. B. Olde Daalhuis. "Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles." SIAM Journal on Mathematical Analysis 50, no. 2 (January 2018): 2144–77. http://dx.doi.org/10.1137/17m1154217.

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39

Bulatov, V. V., and Yu V. Vladimirov. "Asymptotics of the Far Fields of Internal Gravity Waves Excited by a Source of Radial Symmetry." Fluid Dynamics 56, no. 5 (September 2021): 672–77. http://dx.doi.org/10.1134/s0015462821050013.

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Abstract— The problem of the far field of internal gravity waves generated by a perturbation source of radial symmetry aroused at an initial instant of time is solved. The constant model distribution of the buoyancy frequency is considered and, using the Fourier–Hankel transform, an analytical solution to the problem is obtained in the form of the sum of wave modes. Asymptotics of the solutions that describe the spatial-temporal characteristics of elevation of the isopycnic lines and the vertical and horizontal velocity components far from the perturbation source are obtained. The asymptotics of the components of the wave field are expressed in terms of the square of the Airy function and its derivatives in the neighborhood of the wave fronts of an individual wave mode. The exact and asymptotic results are compared and it is shown that the asymptotic method makes it possible to calculate effectively the far wave fields at times of the order of ten and more of the Brunt–Väisälä periods.

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40

Li, Jun, and Yiqiang Q. Zhao. "ON THE PROBABILITY DISTRIBUTION OF JOIN QUEUE LENGTH IN A FORK-JOIN MODEL." Probability in the Engineering and Informational Sciences 24, no. 4 (August 19, 2010): 473–83. http://dx.doi.org/10.1017/s0269964810000112.

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In this article, we consider the two-node fork-join model with a Poisson arrival process and exponential service times of heterogeneous service rates. Using a mapping from the queue lengths in the parallel nodes to the join queue length, we first derive the probability distribution function of the join queue length in terms of joint probabilities in the parallel nodes and then study the exact tail asymptotics of the join queue length distribution. Although the asymptotics of the joint distribution of the queue lengths in the parallel nodes have three types of characterizations, our results show that the asymptotics of the join queue length distribution are characterized by two scenarios: (1) an exact geometric decay and (2) a geometric decay with the prefactor n−1/2.

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41

Sang, Hailin, and Yimin Xiao. "Exact moderate and large deviations for linear random fields." Journal of Applied Probability 55, no. 2 (June 2018): 431–49. http://dx.doi.org/10.1017/jpr.2018.28.

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Abstract By extending the methods of Peligrad et al. (2014), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.

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42

Andrews, Donald W. K., and Patrik Guggenberger. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP." Econometric Theory 26, no. 2 (October 2, 2009): 426–68. http://dx.doi.org/10.1017/s0266466609100051.

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This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set of high-level conditions that are relatively easy to verify. The results show that the asymptotic size of subsampling and m out of n bootstrap tests is distorted in some examples but not in others.

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43

Dai, Hongshuai, Donald A. Dawson, and Yiqiang Q. Zhao. "Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs." ESAIM: Probability and Statistics 26 (2022): 26–68. http://dx.doi.org/10.1051/ps/2021018.

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In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.

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44

MUBAYI, DHRUV. "Some Exact Results and New Asymptotics for Hypergraph Turán Numbers." Combinatorics, Probability and Computing 11, no. 3 (May 2002): 299–309. http://dx.doi.org/10.1017/s0963548301005028.

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Given a family [Fscr ] of r-graphs, let ex(n, [Fscr ]) be the maximum number of edges in an n-vertex r-graph containing no member of [Fscr ]. Let C(r)4 denote the family of r-graphs with distinct edges A, B, C, D, such that A ∩ B = C ∩ D = Ø and A ∪ B = C ∪ D. For s1 [les ] … [les ] sr, let K(r) (s1,…,sr) be the complete r-partite r-graph with parts of sizes s1,…,sr.Füredi conjectured over 15 years ago that ex(n,C(3)4) [les ] (n2) for sufficiently large n. We prove the weaker resultex(n, {C(3)4, K(3)(1,2,4)}) [les ] (n2).Generalizing a well-known conjecture for the Turán number of bipartite graphs, we conjecture thatex(n, K(r)(s1,…,sr)) = Θ(nr−1/s),where s = Πr−1i=1si. We prove this conjecture when s1 = … = sr−2 = 1 and(i) sr−1 = 2, (ii) sr−1 = sr = 3, (iii)sr > (sr−1−1)!.In cases (i) and (ii), we determine the asymptotic value of ex(n,K(r)(s1,…,sr)).We also provide an explicit construction givingex(n,K(3)(2,2,3)) > (1/6−o(1))n8/3.This improves upon the previous best lower bound of Ω(n29/11) obtained by probabilistic methods. Several related open problems are also presented.

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45

Bíró, József. "Novel bandwidth requirement estimation based on exact large deviation asymptotics." Computer Communications 33 (November 2010): S152—S156. http://dx.doi.org/10.1016/j.comcom.2010.04.028.

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Sohn, Eunju, and Charles Knessl. "Storage allocation under processor sharing I: exact solutions and asymptotics." Queueing Systems 65, no. 1 (January 30, 2010): 1–18. http://dx.doi.org/10.1007/s11134-010-9164-3.

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Song, Yang, Zai-ming Liu, and Hong-shuai Dai. "Exact tail asymptotics for a discrete-time preemptive priority queue." Acta Mathematicae Applicatae Sinica, English Series 31, no. 1 (January 2015): 43–58. http://dx.doi.org/10.1007/s10255-015-0448-6.

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Lelarge, M., and A. Villani. "Exact Tail Asymptotics of a Queue with LRD Input Traffic." Journal of Mathematical Sciences 196, no. 1 (December 21, 2013): 57–69. http://dx.doi.org/10.1007/s10958-013-1636-7.

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Fleischmann, Klaus, and Stanislav Alekseevich Molchanov. "Exact asymptotics in a mean field model with random potential." Probability Theory and Related Fields 86, no. 2 (June 1990): 239–51. http://dx.doi.org/10.1007/bf01474644.

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Heemskerk, Mariska, and Michel Mandjes. "Exact asymptotics in an infinite-server system with overdispersed input." Operations Research Letters 47, no. 6 (November 2019): 513–20. http://dx.doi.org/10.1016/j.orl.2019.09.003.

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