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Moments of Markovian growth–collapse processes

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 June 2022

Nicolas Privault Open the ORCID record for Nicolas Privault [Opens in a new window]
Nicolas Privault*
Affiliation:
Nanyang Technological University
*
*Postal address: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371. Email address: nprivault@ntu.edu.sg
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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 moment expressions of all orders. In comparison with other methods based on differential equations, our approach yields explicit summations in terms of the time parameter. We also treat the case of the associated embedded chain, and provide recursive codes in Maple and Mathematica for the computation of moments and cumulants of any order with arbitrary cut-off moment sequences and jump size functions.

Keywords

Growth–collapse processesPoisson shot noiseuniform cut-off ratesstochastic integrals with jumpsmomentscumulants

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J22: Computational methods in Markov chains 60G55: Point processes

Information

Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 4 , December 2022 , pp. 1070 - 1093
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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