PUBLISHED PAPERS #04.03
| Azam Imomov, Sarvar Iskandarov. On Convergence Rate to Invariant Measures in Continuous-Time Critical Markov Branching Systems with Possibly Infinite Variance and Allowing Immigration |
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| Abstract. Markov branching systems belong to an important class of stochastic processes widely used for modeling various phenomena in biology, physics, finance, and other fields. This system is characterized by a state that evolves over continuous time and the possibility of "branching" in each state, in which the system can transition to several different states, not just one. This property is especially important in studying population dynamics, disease spread, and models of random chains with multiple outcomes. Unlike simple Markov systems, branching systems require taking into account not only the transition probabilities between states but also the branching probabilities, which significantly complicates the mathematical description. We discuss the asymptotic properties of the transition functions of Markov branching systems allowing immigration. |
| Keywords: branching systems, immigration, Markov chain, transition functions, generating functions, slowly varying function, invariant measures, convergence rate |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.096 |