Moments and polynomial expansions in discrete matrix-analytic models

Søren Asmussen*, Mogens Bladt

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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.

Original languageEnglish
JournalStochastic Processes and Their Applications
Volume150
Pages (from-to)1165-1188
Number of pages24
ISSN0304-4149
DOIs
Publication statusPublished - Aug 2022

Keywords

  • BMAP
  • Erlangization
  • Factorial moments
  • Matrix exponentials
  • Richardson extrapolation
  • Wiener–Hopf factorization

Fingerprint

Dive into the research topics of 'Moments and polynomial expansions in discrete matrix-analytic models'. Together they form a unique fingerprint.

Cite this