Mutually interacting superprocesses with migration

TL;DR

This paper constructs a new class of superprocesses with migration from branching particle systems and proves their uniqueness via stochastic PDEs with non-Lipschitz coefficients.

Contribution

It introduces a novel framework for mutually interacting superprocesses with migration and establishes their uniqueness through stochastic PDE analysis.

Findings

Superprocesses constructed as limits of branching particle systems.

Uniqueness in law proved using stochastic PDEs with non-Lipschitz coefficients.

Framework applicable to population models with migration.

Abstract

A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the pathwise uniqueness of a system of stochastic partial differential equations with non-Lipschitz coefficients, which is satisfied by the corresponding system of distribution-function-valued processes.