Fluctuation Theory of Continuous-Time, Skip-Free Downward Markov Chains with Applications to Branching Processes with Immigration

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-12 DOI:10.1287/moor.2022.0246

Ronnie Loeffen, Pierre Patie, Jian Wang

引用次数: 0

Abstract

We develop a comprehensive methodology for the fluctuation theory of continuous-time, skip-free Markov chains, extending and improving the recent work of Choi and Patie for discrete-time, skip-free Markov chains. As a significant application, we use it to derive a full set of fluctuation identities regarding exiting a finite or infinite interval for Markov branching processes with immigration, thereby uncovering many new results for this classic family of continuous-time Markov chains. The theory also allows us to recover in a simple manner fluctuation identities for skip-free downward compound Poisson processes.

查看原文本刊更多论文

连续时间、无跳跃向下马尔可夫链的波动理论及其在有移民的分支过程中的应用

我们为连续时间无跳马尔可夫链的波动理论开发了一种全面的方法论，扩展并改进了 Choi 和 Patie 最近针对离散时间无跳马尔可夫链的工作。一个重要的应用是，我们用它推导出了有移民的马尔科夫分支过程退出有限或无限区间的全套波动特性，从而为这个经典的连续时间马尔科夫链家族揭示了许多新结果。该理论还使我们能够以简单的方式恢复无跳向下复合泊松过程的波动特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.