The probability of reaching a receding boundary by branching random walk with fading branching and heavy-tailed jump distribution

Pavel Tesemnikov; Sergey Foss

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arXiv · 2110.10544

The probability of reaching a receding boundary by branching random walk with fading branching and heavy-tailed jump distribution

Pavel Tesemnikov·Sergey Foss

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Abstract

Foss and Zachary (2003) and Foss, Palmowski and Zachary (2005) studied the probability of achieving a receding boundary on a time interval of random length by a random walk with a heavy-tailed jump distribution. They have proposed and developed a new approach that allows to generalise results of Asmussen (1998) onto the case of arbitrary stopping times and a wide class of nonlinear boundaries, and to obtain uniform results over all stopping times. In this paper, we consider a class of branching random walks with fading branching and obtain results on the tail asymptotics for the maximum of a branching random walk on a time interval of random (possibly unlimited) length, as well as uniform results within a class of bounded random time intervals.

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Pavel Tesemnikov, Sergey Foss. 2021-10-20. The probability of reaching a receding boundary by branching random walk with fading branching and heavy-tailed jump distribution. https://arxiv.org/abs/2110.10544

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