$L\log L$ condition for supercritical branching Hunt processes

TL;DR

This paper extends the Kesten-Stigum $L ext{-} extlog L$ theorem to supercritical branching Hunt processes using spine decomposition and martingale change of measure, generalizing previous results for diffusions.

Contribution

It introduces a new $L ext{-} extlog L$ criterion for branching Hunt processes, broadening the applicability of the theorem beyond diffusions.

Findings

Established an $L ext{-} extlog L$ criterion for supercritical branching Hunt processes

Generalized classical results from diffusions to Hunt processes

Utilized spine decomposition and martingale change of measure techniques

Abstract

In this paper we use the spine decomposition and martingale change of measure to establish a Kesten-Stigum $L\log L$ theorem for branching Hunt processes. This result is a generalization of the results in Asmussen-Hering (1976) and Hering (1978) for branching diffusions.