Maximal displacement of branching symmetric stable processes

TL;DR

This paper analyzes the maximum displacement in a branching symmetric stable process with complex, inhomogeneous branching rates, providing explicit tail behavior and limiting distribution insights.

Contribution

It introduces a detailed analysis of maximal displacement for processes with singular, spatially inhomogeneous branching structures, including explicit tail behavior and distribution results.

Findings

Derived the limiting distribution of maximal displacement

Established explicit tail behavior for the process

Handled singular and inhomogeneous branching rates

Abstract

We determine the limiting distribution and the explicit tail behavior for the maximal displacement of a branching symmetric stable process with spatially inhomogeneous branching structure. Here the branching rate is a Kato class measure with compact support and can be singular with respect to the Lebesgue measure.