Moments and polynomial expansions in discrete matrix-analytic models

Autor:	Søren Asmussen, Mogens Bladt
Rok vydání:	2022
Předmět:	Statistics and Probability BMAP Richardson extrapolation Matrix exponentials Erlangization Applied Mathematics Modeling and Simulation Wiener–Hopf factorization Factorial moments
Zdroj:	Asmussen, S & Bladt, M 2022, ' Moments and polynomial expansions in discrete matrix-analytic models ', Stochastic Processes and Their Applications, vol. 150, pp. 1165-1188 . https://doi.org/10.1016/j.spa.2021.12.002
ISSN:	0304-4149
DOI:	10.1016/j.spa.2021.12.002
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::37392a804608c17de28bfff8a5f58781 https://doi.org/10.1016/j.spa.2021.12.002 Zobrazit plný text záznamu Full Text from ScienceDirect