On Distributions of Certain State-Dependent Fractional Point Processes

K. K. Kataria () and P. Vellaisamy ()
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K. K. Kataria: Indian Institute of Technology Bombay
P. Vellaisamy: Indian Institute of Technology Bombay

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1554-1580

Abstract: 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.

Keywords: State-dependent fractional pure birth process; State-dependent time fractional Poisson process; Time fractional Poisson process; 60G22; 60G55 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0835-z

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