On the maximal displacement of subcritical branching random walks with or without killing
Abstract
Consider a subcritical branching random walk {Zk}k≥0 with offspring distribution {pk}k≥0 and step size X. Let Mn denote the rightmost position reached by {Zk}k≥0 up to generation n, and define M:=supn≥0Mn. In this paper we give asymptotics of the tail probability of M under optimal assumptions ∑k=1∞(klogk)pk
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Stochastic processes and financial applications
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–29
- Publication date
- 1 January 2026
- Language
- EN