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This article is cited in 9 scientific papers (total in 9 papers)
On the Asymptotic Behavior of Distributions of First-Passage Times, II
A. A. Borovkov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
In this paper, the asymptotic behavior of and estimates for the distribution of first-passage times for a random walk with nonzero drift are obtained in the case of passage of zero level (in both directions).
DOI:
https://doi.org/10.4213/mzm37
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English version:
Mathematical Notes, 2004, 75:3, 322–330
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UDC:
519.214
Received: 17.05.2002
Revised: 01.04.2003
Citation:
A. A. Borovkov, “On the Asymptotic Behavior of Distributions of First-Passage Times, II”, Mat. Zametki, 75:3 (2004), 350–359; Math. Notes, 75:3 (2004), 322–330
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz37https://doi.org/10.4213/mzm37 http://mi.mathnet.ru/eng/mz/v75/i3/p350
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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
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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
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Vatutin V.A., Wachtel V., “Local probabilities for random walks conditioned to stay positive”, Probab. Theory Related Fields, 143:1-2 (2009), 177–217
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Denisov D., Shneer V., “Asymptotics for the First Passage Times of Levy Processes and Random Walks”, J. Appl. Probab., 50:1 (2013), 64–84
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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
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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
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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
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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
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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
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