Poisson random measures and supercritical multitype Markov branching processes

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-01-21 DOI:10.1080/15326349.2021.2016446

M. Slavtchova-Bojkova, O. Hyrien, N. Yanev

引用次数: 1

Abstract

Abstract We consider multitype Markov branching processes with immigration occurring at time points generated by Poisson random measures. These models find applications to study evolution of multitype cell populations in which new cells join the population according to a time-varying immigration mechanism. The focus of this paper is the supercritical case. We investigate the limiting behavior of the process for different rates of the Poisson random measures. In particular, we prove a result analogous to a strong LLN and establish limiting normal distributions.

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Poisson随机测度与超临界多类型Markov分支过程

摘要我们考虑了在泊松随机测度生成的时间点上发生迁移的多类型马尔可夫分支过程。这些模型可应用于研究多类型细胞群体的进化，其中新细胞根据时变迁移机制加入群体。本文的重点是超临界情况。我们研究了不同泊松随机测度率下过程的极限行为。特别地，我们证明了一个类似于强LLN的结果，并建立了极限正态分布。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.