Submartingale Condition for Weak Convergence for Semi-Markov Processes

2025/12/28 by Vitaliy Golomoziy, Golomoziy, Vitaliy
Decision Sciences · Economics, Econometrics and Finance · #60B10 #60K15 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2512.22836

openalex publication_date 2025/12/28 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28

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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