下无跳跃马尔可夫链拟平稳分布的存在性

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-01-27 DOI:10.1016/j.spa.2025.104579

Kosuke Yamato

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引用次数: 0

摘要

研究了非负整数上无向下跳跃的连续时间马尔可夫链的准平稳分布的存在性。引入了过程的尺度函数，并根据尺度函数的可积性条件对边界进行了分类，推广了Feller关于生死过程边界的分类方法。用尺度函数和边界的新分类来表征拟平稳分布的存在性和集。

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Existence of quasi-stationary distributions for downward skip-free Markov chains

For downward skip-free continuous-time Markov chains on non-negative integers killed at zero, the existence of the quasi-stationary distribution is studied. The scale function for the process is introduced, and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes. The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.