Moments of continuous-state branching processes with or without immigration

TL;DR

This paper investigates the conditions under which moments of continuous-state branching processes, with or without immigration, exist, using stochastic equations for characterization.

Contribution

It provides new criteria for the existence of moments in continuous-state branching processes, extending previous stochastic equation characterizations.

Findings

Criteria for the existence of f-moments established

Characterization of processes via stochastic equations used in proofs

Results applicable to processes with or without immigration

Abstract

For a positive continuous function f satisfying some standard conditions, we study the f-moments of continuous-state branching processes with or without immigration. The main results give criteria for the existence of the f-moments. The characterization of the processes in terms of stochastic equations given by Dawson and Li (2012) plays an essential role in the proofs.