Geometric branching reproduction Markov processes

• Main Authors: Assen Tchorbadjieff, Penka Mayster
• Format: Article
• Language: English
• Published: VTeX 2020-09-01
• Series: Modern Stochastics: Theory and Applications
• Subjects: branching process; lagrange inversion; gauss hypergeometric; wright; lambert-w functions; extinction probability
• Online Access: https://www.vmsta.org/doi/10.15559/20-VMSTA163
• ISSN: 2351-6046; 2351-6054

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.