Moments and polynomial expansions in discrete matrix-analytic models
Research output: Contribution to journal › Journal article › Research › peer-review
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 language | English |
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Journal | Stochastic Processes and Their Applications |
Volume | 150 |
Pages (from-to) | 1165-1188 |
ISSN | 0304-4149 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© 2021 Elsevier B.V.
- BMAP, Erlangization, Factorial moments, Matrix exponentials, Richardson extrapolation, Wiener–Hopf factorization
Research areas
ID: 289461005