Geometric branching reproduction Markov processes
Volume 7, Issue 4 (2020), pp. 357–378
Pub. online: 30 September 2020
Type: Research Article
Open Access
Open Access
Received
7 June 2020
7 June 2020
Revised
20 September 2020
20 September 2020
Accepted
20 September 2020
20 September 2020
Published
30 September 2020
30 September 2020
Abstract
We present a model of a continuous-time Markov branching process with the infinitesimal generating function defined by the geometric probability distribution. It is proved that the solution of the backward Kolmogorov equation is expressed by the composition of special functions – Wright function in the subcritical case and Lambert-W function in the critical case. We found the explicit form of conditional limit distribution in the subcritical branching reproduction. In the critical case, the extinction probability and probability mass function are expressed as a series containing Bell polynomial, Stirling numbers, and Lah numbers.
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