Submartingale condition for weak convergence for semi-Markov processes
Pub. online: 24 February 2026
Type: Research Article
Open Access
Open Access
Received
21 September 2025
21 September 2025
Revised
27 December 2025
27 December 2025
Accepted
10 February 2026
10 February 2026
Published
24 February 2026
24 February 2026
Abstract
In this paper, we consider a modified version of a well-known submartingale condition for the weak convergence of probability measures, 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.
References
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