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

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations 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.

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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。

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来源期刊

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.