The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution

P. I. Tesemnivkov ; S. G. Foss

Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 336-354.

Résumé

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 one to generalise the results of Asmussen (1998) to the case of arbitrary stopping times and to 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.

Détail

Keywords: subexponential and strong subexponential distributions, branching random walk, receding boundary, principle of a single big jump.

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