Geometric branching reproduction Markov processes

Published: 30 September 2020
by  VTeX
Modern Stochastics: Theory and Applications pp 1-22; doi:10.15559/20-vmsta163

Abstract: Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Geometric branching reproduction Markov processes, Authors: Assen Tchorbadjieff, Penka Mayster , 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.
Keywords: Function / model / publishing / Markov / solutions / subcritical / geometric / branching reproduction