The Probability of Exceeding a High Boundary on a Random Time Interval for a Heavy-tailed Random Walk by Serguei Foss,1 Zbigniew Palmowski2 and Stan Zachary
نویسندگان
چکیده
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.
منابع مشابه
The Probability of Exceeding a High Boundary on a Random Time Interval for a Heavy-tailed Random Walk
We study the asymptotic probability that a random walk with heavy-tailed 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 counterexam...
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