The probability of exceeding a High boundary on a random time interval for a heavy-tailed random walk

Serguei Fos; Zbigniew Palmowski; Stan Zachary

doi:10.1214/105051605000000269

The probability of exceeding a High boundary on a random time interval for a heavy-tailed random walk

Serguei Fos, Zbigniew Palmowski, Stan Zachary

Research output: Contribution to journal › Literature review › peer-review

27 Citations (Scopus)

Abstract

We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. © Institute of Mathematical Statistics, 2005.

Original language	English
Pages (from-to)	1936-1957
Number of pages	22
Journal	Annals of Applied Probability
Volume	15
Issue number	3
DOIs	https://doi.org/10.1214/105051605000000269
Publication status	Published - Aug 2005

Keywords

Boundary
Random walk
Ruin probability
Subexponential distributions

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10.1214/105051605000000269

Cite this

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abstract = "We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. {\textcopyright} Institute of Mathematical Statistics, 2005.",

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N2 - We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. © Institute of Mathematical Statistics, 2005.

AB - We study the asymptotic probability that a random walk with heavytailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples. © Institute of Mathematical Statistics, 2005.

KW - Boundary

KW - Random walk

KW - Ruin probability

KW - Subexponential distributions

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DO - 10.1214/105051605000000269

M3 - Literature review

VL - 15

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EP - 1957

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 3

ER -

The probability of exceeding a High boundary on a random time interval for a heavy-tailed random walk

Abstract

Keywords

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