Factorial moments of the critical Markov branching process with geometric reproduction of particles
Volume 9, Issue 2 (2022), pp. 229–244
Pub. online: 7 February 2022
Type: Research Article
Open Access
Open Access
Received
30 June 2021
30 June 2021
Revised
26 November 2021
26 November 2021
Accepted
24 January 2022
24 January 2022
Published
7 February 2022
7 February 2022
Abstract
The factorial moments of any Markov branching process describe the behaviour of its probability generating function $F(t,s)$ in the neighbourhood of the point $s=1$. They are applied to solve the forward Kolmogorov equation for the critical Markov branching process with geometric reproduction of particles. The solution includes quickly convergent recurrent iterations of polynomials. The obtained results on factorial moments enable computation of statistical measures as shape and skewness. They are also applicable to the comparison between critical geometric branching and linear birth-death processes.
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