亚临界马尔可夫分支过程中的扩展Sibuya分布

IF 0.3 4区综合性期刊 Q4 MULTIDISCIPLINARY SCIENCES

Comptes Rendus De L Academie Bulgare Des Sciences Pub Date : 2023-04-30 DOI:10.7546/crabs.2023.04.02

Penka Mayster, Assen Tchorbadjieff

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引用次数: 0

摘要

以一个粒子为初始条件的亚临界马尔可夫分支过程X(t)的最终消光概率为q = 1。所考虑的分支机制由非负整数上的对数分布的混合定义。本文的目的是证明在这种情况下，在时间t >时存活的粒子的随机数X(t);0遵循位移扩展的Sibuya分布，参数取决于时间t >0. 条件极限概率是由正整数支持的对数级数分布。

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Extended Sibuya Distribution in Subcritical Markov Branching Processes

The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions on the nonnegative integers. The purpose of the present paper is to prove that in this case the random number of particles X(t) alive at time t > 0 follows the shifted extended Sibuya distribution, with parameters depending on the time t > 0. The conditional limit probability is the logarithmic series distribution supported by the positive integers.

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来源期刊

Comptes Rendus De L Academie Bulgare Des Sciences 综合性期刊-综合性期刊

CiteScore

0.60

自引率

33.30%

发文量

181

审稿时长

3-6 weeks

期刊介绍： Founded in 1948 by academician Georgy Nadjakov, "Comptes rendus de l’Académie bulgare des Sciences" is also known as "Доклади на БАН","Доклады Болгарской академии наук" and "Proceeding of the Bulgarian Academy of Sciences". If applicable, the name of the journal should be abbreviated as follows: C. R. Acad. Bulg. Sci. (according to ISO)