Stochastic equations and ergodicity for two‐type continuous‐state branching processes with immigration in Lévy random environments

Abstract

This paper establishes a stochastic differential equation system with both positive and negative jumps and proves the existence and uniqueness of the strong solution and presents an equivalent condition for ergodicity of the solution. The strong solution is called two‐type continuous‐state branching processes with immigration in Lévy random environments. The model can be extended to any finite dimensional case.