Submartingale condition for weak convergence for semi-Markov processes
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.
Fields of Study & Subjects
Probability and Statistical Research
Stochastic processes and statistical mechanics
Probability and Risk Models
Publication details
- Journal / source
- Modern Stochastics Theory and Applications
- Pages
- 275–287
- Publication date
- 1 January 2026
- Language
- EN