Submartingale Condition for Weak Convergence for Semi-Markov Processes

Vitaliy Golomoziy

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arXiv · 2512.22836

Submartingale Condition for Weak Convergence for Semi-Markov Processes

Vitaliy Golomoziy

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Abstract

In this paper, we consider a modified version of a well-known submartingale condition fortheweak convergence of probabilitymeasures, adapted to the semi-Markov case. In this setting, it is convenient to work with an embedded Markov chain and the filtration generated by jump times. We demonstrate that a straightforward restatement of the classical result is not valid, and that an additional condition is required.

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Vitaliy Golomoziy. 2025-12-28. Submartingale Condition for Weak Convergence for Semi-Markov Processes. https://arxiv.org/abs/2512.22836

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