A. A. Borovkov, “On the Asymptotic Behavior of the Distributions of First-Passage Times, I”, Mat. Zametki, 75:1 (2004), 24–39; Math. Notes, 75:1 (2004), 23

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Matematicheskie Zametki, 2004, Volume 75, Issue 1, Pages 24–39
DOI: https://doi.org/10.4213/mzm4 (Mi mzm4)

This article is cited in 21 scientific papers (total in 21 papers)

On the Asymptotic Behavior of the Distributions of First-Passage Times, I

A. A. Borovkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Full-text PDF (256 kB) Citations (21)

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DOI: https://doi.org/10.4213/mzm4

Abstract: In this paper, the asymptotic behavior of and estimates for the distribution of first-passage times for a random walk are obtained in the cases of fixed and increasing levels. In the first part of the paper, the case of zero level is studied.

Received: 17.05.2002
Revised: 01.04.2003

English version:
Mathematical Notes, 2004, Volume 75, Issue 1, Pages 23–37
DOI: https://doi.org/10.1023/B:MATN.0000015019.37128.cb

Bibliographic databases:

UDC: 519.214

Language: Russian

Citation: A. A. Borovkov, “On the Asymptotic Behavior of the Distributions of First-Passage Times, I”, Mat. Zametki, 75:1 (2004), 24–39; Math. Notes, 75:1 (2004), 23–37

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm4

https://doi.org/10.4213/mzm4

https://www.mathnet.ru/eng/mzm/v75/i1/p24

Cycle of papers

On the Asymptotic Behavior of the Distributions of First-Passage Times, I
A. A. Borovkov
Mat. Zametki, 2004, 75:1, 24–39
On the Asymptotic Behavior of Distributions of First-Passage Times, II
A. A. Borovkov
Mat. Zametki, 2004, 75:3, 350–359

This publication is cited in the following 21 articles:

Ion Grama, Hui Xiao, “Conditioned local limit theorems for random walks on the real line”, Ann. Inst. H. Poincaré Probab. Statist., 61:1 (2025)
ION GRAMA, JEAN-FRANÇOIS QUINT, HUI XIAO, “Conditioned limit theorems for hyperbolic dynamical systems”, Ergod. Th. Dynam. Sys., 44:1 (2024), 50
Grama I. Lauvergnat R. Le Page E., “Conditioned Local Limit Theorems For Random Walks Defined on Finite Markov Chains”, Probab. Theory Relat. Field, 176:1-2 (2020), 669–735
Berger Q., “Notes on Random Walks in the Cauchy Domain of Attraction”, Probab. Theory Relat. Field, 175:1-2 (2019), 1–44
Grama I. Lauvergnat R. Le Page E., “Limit Theorems For Markov Walks Conditioned to Stay Positive Under a Spectral Gap Assumption”, Ann. Probab., 46:4 (2018), 1807–1877
Ion Grama, Ronan Lauvergnat, Émile Le Page, “Limit theorems for affine Markov walks conditioned to stay positive”, Ann. Inst. H. Poincaré Probab. Statist., 54:1 (2018)
R. T. Aliev, T. A. Khaniev, “On the Limiting Behavior of the Characteristic Function of the Ergodic Distribution of the Semi-Markov Walk with Two Boundaries”, Math. Notes, 102:4 (2017), 444–454
Grama I. Le Page E. Peigne M., “Conditioned Limit Theorems For Products of Random Matrices”, Probab. Theory Relat. Field, 168:3-4 (2017), 601–639
Ion Grama, Springer Proceedings in Mathematics & Statistics, 208, Modern Problems of Stochastic Analysis and Statistics, 2017, 93
Ion Grama, Émile Le Page, Springer Proceedings in Mathematics & Statistics, 208, Modern Problems of Stochastic Analysis and Statistics, 2017, 103
Aurzada F. Kramm T., “The First Passage Time Problem Over a Moving Boundary for Asymptotically Stable Lévy Processes”, J. Theor. Probab., 29:3 (2016), 737–760
Aurzada F. Kramm T. Savov M., “First Passage Times of Levy Processes Over a One-Sided Moving Boundary”, Markov Process. Relat. Fields, 21:1 (2015), 1–38
I. Unver, Ya. S. Tundzh, E. Ibaev, “Laplace-Stieltjes transform of the distribution of the first moment of crossing the level a(a > 0) by a semi-Markovian random walk with positive drift and negative jumps”, Aut. Control Comp. Sci., 48:3 (2014), 144
Denisov D. Shneer V., “Asymptotics for the First Passage Times of Levy Processes and Random Walks”, J. Appl. Probab., 50:1 (2013), 64–84
Denis Denisov, Vsevolod Shneer, “Asymptotics for the First Passage Times of Lévy Processes and Random Walks”, J. Appl. Probab., 50:01 (2013), 64
A. A. Mogul'skii, “Local limit theorem for the first crossing time of a fixed level by a random walk”, Siberian Adv. Math., 20:3 (2010), 191–200
Denisov, D, “Local asymptotics of the cycle maximum of a heavy-tailed random walk”, Advances in Applied Probability, 39:1 (2007), 221
Denis Denisov, Vsevolod Shneer, “Local asymptotics of the cycle maximum of a heavy-tailed random walk”, Adv. Appl. Probab., 39:01 (2007), 221
A. A. Mogul'skii, “Large deviations of the first passage time for a random walk with semiexponentially distributed jumps”, Siberian Math. J., 47:6 (2006), 1084–1101
A. A. Mogul'skii, B. A. Rogozin, “A Local Theorem for the First Hitting Time of a Fixed Level by a Random Walk”, Siberian Adv. Math., 15:3 (2005), 1–27

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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