Moments and polynomial expansions in discrete matrix-analytic models

Søren Asmussen and Mogens Bladt

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1165-1188

Abstract: Calculation of factorial moments and point probabilities is considered in integer-valued matrix-analytic models at a finite horizon T. Two main settings are considered, maxima of integer-valued downward skipfree Lévy processes and Markovian point process with batch arrivals (BMAPs). For the moments of the finite-time maxima, the procedure is to approximate the time horizon T by an Erlang distributed one and solve the corresponding matrix Wiener–Hopf factorization problem. For the BMAP, a structural matrix-exponential representation of the factorial moments of N(T) is derived. Moments are then used as a computational vehicle to provide a converging Gram–Charlier series for the point probabilities. Topics such as change-of-measure techniques and time inhomogeneity are also discussed.

Keywords: BMAP; Erlangization; Factorial moments; Matrix exponentials; Richardson extrapolation; Wiener–Hopf factorization (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:150:y:2022:i:c:p:1165-1188

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DOI: 10.1016/j.spa.2021.12.002

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