On the Separating Variables Method for Markov Death-Process Equations

Aleksandr V. Kalinkin () and Anton V. Mastikhin ()
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Aleksandr V. Kalinkin: Bauman Moscow State Technical University
Anton V. Mastikhin: Bauman Moscow State Technical University

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 163-182

Abstract: Abstract We consider a method of obtaining non-closed solutions of the first and second Kolmogorov equations for the exponential (double) generating function of transition probabilities for quadratic death-processes of one, two and three dimensions. We obtain a representation for the generating function of transition probabilities in the form of a Fourier series, using generalized hypergeometric functions and Jacobi polynomials.

Keywords: Markov death-process; Transition probabilities; Equations for exponential generating function; Exact solutions; Special functions; Branching property; 60J27; 60J80; 60K35 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-017-0795-8

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