Enhanced Asymptotic Analysis of Continuous-Time Markov Branching Systems: Revisiting Limiting Structural Theorems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915906602401792 |
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| author | Imomov, Azam A Iskandarov, Sarvar B. Azimov, Jakhongir B. Jumaqulov, Hurshidjon Q. |
| author_facet | Imomov, Azam A Iskandarov, Sarvar B. Azimov, Jakhongir B. Jumaqulov, Hurshidjon Q. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01257 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Enhanced Asymptotic Analysis of Continuous-Time Markov Branching Systems: Revisiting Limiting Structural Theorems Imomov, Azam A Iskandarov, Sarvar B. Azimov, Jakhongir B. Jumaqulov, Hurshidjon Q. Probability 60J80, 60J85 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. |
| title | Enhanced Asymptotic Analysis of Continuous-Time Markov Branching Systems: Revisiting Limiting Structural Theorems |
| topic | Probability 60J80, 60J85 |
| url | https://arxiv.org/abs/2604.01257 |