Two-type continuous-state branching processes in varying environments

TL;DR

This paper constructs a class of two-type continuous-state branching processes in changing environments by solving backward equations, allowing for time-varying parameters and overcoming bottleneck challenges with moment conditions.

Contribution

It introduces a novel construction method for two-type continuous-state branching processes with time-varying parameters in changing environments.

Findings

Successfully constructed the process using backward equations.

Handled time-varying parameters with cdlg functions.

Overcame bottleneck issues through a specific moment condition.

Abstract

A basic class of two-type continuous-state branching processes in varying environments are constructed by solving the backward equation determining the cumulant semigroup. The parameters of the process are allowed to be c\`adl\`ag in time and the difficulty brought about by the bottlenecks are overcome by introducing a suitable moment condition.