Law of large numbers for supercritical superprocesses with non-local branching

TL;DR

This paper proves weak and strong laws of large numbers for supercritical superprocesses with non-local branching, extending previous results to more general models including multitype and discontinuous spatial processes.

Contribution

It introduces laws of large numbers for superprocesses with non-local branching, broadening the scope beyond local branching models.

Findings

Established weak and strong laws of large numbers for non-local superprocesses

Extended results to multitype continuous-state branching processes and superdiffusions

Included examples with discontinuous spatial motions and complex branching mechanisms

Abstract

In this paper we establish a weak and a strong law of large numbers for supercritical superprocesses with general non-local branching mechanisms. Our results complement earlier results obtained for superprocesses with only local branching. Several interesting examples are developed, including multitype continuous-state branching processes, multitype superdiffusions and superprocesses with discontinuous spatial motions and non-decomposable branching mechanisms.