Extended Sibuya Distribution in Subcritical Markov Branching Processes
Keywords:branching process, mixture of logarithmic distributions, extended Sibuya distribution, conditional limit probability
The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions on the nonnegative integers. The purpose of the present paper is to prove that in this case the random number of particles X(t) alive at time t > 0 follows the shifted extended Sibuya distribution, with parameters depending on the time t > 0. The conditional limit probability is the logarithmic series distribution supported by the positive integers.
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LicenseCopyright (c) 2023 Proceedings of the Bulgarian Academy of Sciences
Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
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