## Abstract

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 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.

Original language | English |
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Pages (from-to) | 318-335 |

Number of pages | 18 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 316 |

Issue number | 1 |

DOIs | |

Publication status | Published - 27 Apr 2022 |

## Keywords

- branching random walk
- principle of a single big jump
- receding boundary
- subexponential and strong subexponential distributions

## ASJC Scopus subject areas

- Mathematics (miscellaneous)