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On Distributions of Certain State-Dependent Fractional Point Processes

On Distributions of Certain State-Dependent Fractional Point Processes We obtain the explicit expressions for the state probabilities of various state-dependent versions of fractional point processes. The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference-differential equations governing the state probabilities of these state-dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Theoretical Probability Springer Journals

On Distributions of Certain State-Dependent Fractional Point Processes

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Probability Theory and Stochastic Processes; Statistics, general
ISSN
0894-9840
eISSN
1572-9230
DOI
10.1007/s10959-018-0835-z
Publisher site
See Article on Publisher Site

Abstract

We obtain the explicit expressions for the state probabilities of various state-dependent versions of fractional point processes. The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference-differential equations governing the state probabilities of these state-dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results.

Journal

Journal of Theoretical ProbabilitySpringer Journals

Published: Jun 5, 2018

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