Journal of Theoretical Probability

, Volume 32, Issue 1, pp 163–182 | Cite as

On the Separating Variables Method for Markov Death-Process Equations

  • Aleksandr V. KalinkinEmail author
  • Anton V. Mastikhin


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.


Markov death-process Transition probabilities Equations for exponential generating function Exact solutions Special functions Branching property 

Mathematics Subject Classification (2010)

60J27 60J80 60K35 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of ‘Higher Mathematics’Bauman Moscow State Technical UniversityMoscowRussia

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