Moments and polynomial expansions in discrete matrix-analytic models

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

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

Harvard

Asmussen, S & Bladt, M 2022, 'Moments and polynomial expansions in discrete matrix-analytic models', Stochastic Processes and Their Applications, bind 150, s. 1165-1188. https://doi.org/10.1016/j.spa.2021.12.002

APA

Asmussen, S., & Bladt, M. (2022). Moments and polynomial expansions in discrete matrix-analytic models. Stochastic Processes and Their Applications, 150, 1165-1188. https://doi.org/10.1016/j.spa.2021.12.002

Vancouver

Asmussen S, Bladt M. Moments and polynomial expansions in discrete matrix-analytic models. Stochastic Processes and Their Applications. 2022;150:1165-1188. https://doi.org/10.1016/j.spa.2021.12.002

Author

Asmussen, Søren ; Bladt, Mogens. / Moments and polynomial expansions in discrete matrix-analytic models. I: Stochastic Processes and Their Applications. 2022 ; Bind 150. s. 1165-1188.

Bibtex

@article{f8d9be8f6eaa44dcb5ad56efd7360da5,
title = "Moments and polynomial expansions in discrete matrix-analytic models",
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 L{\'e}vy 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",
author = "S{\o}ren Asmussen and Mogens Bladt",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2022",
doi = "10.1016/j.spa.2021.12.002",
language = "English",
volume = "150",
pages = "1165--1188",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",

}

RIS

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