Moment properties for two-type continuous-state branching processes in random environments

TL;DR

This paper derives recursive formulas for moments of two-type continuous-state branching processes in Lévy random environments, showing moments are polynomial functions of initial values and establishing criteria for their existence.

Contribution

It introduces recursive moment formulas and existence criteria for moments in two-type continuous-state branching processes within Lévy random environments.

Findings

The nth moment is a polynomial of initial value with degree at most n.

Criteria for the existence of moments are established.

Recursive formulas facilitate analysis of process properties.

Abstract

We first derive the recurisions for integer moments of two-type continuous-state branching processes in L\'{e}vy random environments. Result shows that the $n$th moment of the process is a polynomial of the initial value of the process with at most $n$ degree. Under some natural condition, the criteria for the existence of $f$-moment of the process are also proved.