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

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