Moments of Markovian growth-collapse processes

TL;DR

This paper derives closed-form expressions for all moments of Markovian growth-collapse processes using Poisson stochastic integral identities, providing a polynomial-time approach superior to differential equation methods.

Contribution

It introduces a novel method to compute moments of growth-collapse processes using Poisson stochastic integrals, extending previous mean and variance formulas to all moments.

Findings

Closed-form moments for all orders derived

Polynomial expressions in time parameter obtained

Applicable to embedded chains of the process

Abstract

We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the literature to closed form moments expressions of all orders. In comparison with other methods based on differential equations, our approach yields polynomial expressions in the time parameter. We also treat the case of the associated embedded chain.