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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.10235 |
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Table of Contents:
- Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $μ$. There are several sufficient conditions in the literature which guarantee convergence of all or $μ$-almost all transition probabilities to $μ$ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively $μ$-almost all transition probabilities. In addition, we discuss so-called generalized couplings.