Submartingale Condition for Weak Convergence for Semi-Markov Processes
Probability
2025-12-30 v1
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.
Cite
@article{arxiv.2512.22836,
title = {Submartingale Condition for Weak Convergence for Semi-Markov Processes},
author = {Vitaliy Golomoziy},
journal= {arXiv preprint arXiv:2512.22836},
year = {2025}
}