Moments and polynomial expansions in discrete matrix-analytic models
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Moments and polynomial expansions in discrete matrix-analytic models. / Asmussen, Søren; Bladt, Mogens.
I: Stochastic Processes and Their Applications, Bind 150, 2022, s. 1165-1188.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Moments and polynomial expansions in discrete matrix-analytic models
AU - Asmussen, Søren
AU - Bladt, Mogens
N1 - Publisher Copyright: © 2021 Elsevier B.V.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - BMAP
KW - Erlangization
KW - Factorial moments
KW - Matrix exponentials
KW - Richardson extrapolation
KW - Wiener–Hopf factorization
U2 - 10.1016/j.spa.2021.12.002
DO - 10.1016/j.spa.2021.12.002
M3 - Journal article
AN - SCOPUS:85121784807
VL - 150
SP - 1165
EP - 1188
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 289461005