用随机步过程的极限定理对受控分支过程进行扩散逼近

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2021-12-18 DOI:10.1080/15326349.2022.2066131

Miguel González, Pedro Martín-Chávez, I. D. del Puerto

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引用次数: 1

摘要

摘要受控分支过程（CBP）是对标准Bienaymé–Galton–Watson过程的修改，其中每一代中的祖细胞数量由随机机制决定。我们认为CBP是从随机数目的初始个体开始的。本文的主要目的是提供临界CBP的Feller扩散近似。Sriram等人先前已经证明了通过使用算子半群收敛定理考虑固定数量的初始个体的类似结果。（随机过程应用2007；117:928–946）。利用随机步过程的极限定理，现在提供了另一种证明。

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Diffusion approximation of controlled branching processes using limit theorems for random step processes

Abstract A controlled branching process (CBP) is a modification of the standard Bienaymé–Galton–Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random number of initial individuals. The main aim of this article is to provide a Feller diffusion approximation for critical CBPs. A similar result by considering a fixed number of initial individuals by using operator semigroup convergence theorems has been previously proved by Sriram et al. (Stochastic Processes Appl. 2007;117:928–946). An alternative proof is now provided making use of limit theorems for random step processes.

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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.