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1 results

  • Moments of Markovian growth–collapse processes

  • Part of
  • Nicolas Privault
  • Journal:
    Advances in Applied Probability / Volume 54 / Issue 4 / December 2022
    Published online by Cambridge University Press:
    14 June 2022, pp. 1070-1093
    Print publication:
    December 2022

  • 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.