Enhanced asymptotic analysis of continuous-time Markov branching systems: Revisiting limiting structural theorems

Azam A. Imomov, Sarvar B. Iskandarov, Jakhongir B. Azimov and Hurshidjon Q. Jumaqulov

Chaos, Solitons & Fractals, 2025, vol. 200, issue P2

Abstract: Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching structure, allowing transitions to multiple states from a single one. This branching mechanism plays a critical role in modeling phenomena such as population dynamics, epidemic spread, and probabilistic systems with multiple outcomes. Unlike standard Markov processes, branching systems require a simultaneous treatment of transition dynamics and branching probabilities, resulting in a more intricate mathematical framework. In this work, we investigate the asymptotic properties of transition functions in continuous-time Markov branching-immigration systems. Our focus lies in refining known limit theorems, establishing convergence rates, and deriving improved asymptotic expansions under relaxed moment conditions. The results contribute to a deeper understanding of the long-term behavior and invariant structures within these systems.

Keywords: Markov branching systems; Immigration; Markov chain; Transition functions; Generating functions; Slow variation; Invariant measures; Limit theorems; Convergence rate (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010926

DOI: 10.1016/j.chaos.2025.117079

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