Stochastic equations for two-type continuous-state branching processes in varying environments

TL;DR

This paper constructs a two-type continuous-state branching process in changing environments using stochastic equations driven by time-space noises, and characterizes certain functionals of the process through Laplace transforms.

Contribution

It introduces a novel construction of two-type branching processes in varying environments via stochastic equations with pathwise uniqueness, and provides functional characterizations.

Findings

Successful construction of the process as a unique solution

Characterization of positive integral functionals via Laplace transforms

Establishment of comparison properties for solutions

Abstract

A two-type continuous-state branching process in varying environments is constructed as the pathwise unique solution of a system of stochastic equations driven by time-space noises, where the pathwise uniqueness is derived from a comparison property of solutions. As an application of the main result, we give characterizations of some positive integral functionals of the process in terms of Laplace transforms.