Convergence to quasi-stationarity through Poincar�� inequalities and Bakry-Emery criteria
| Autor: | O��afrain, William |
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| Rok vydání: | 2020 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2001.07794 |
| Popis: | This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincar�� inequality related to a suitable Doob transform entails exponential convergence of conditioned distributions to a quasi-stationary distribution in total variation and in $1$-Wasserstein distance. A special attention is paid to multi-dimensional diffusion processes, for which the aforementioned Poincar�� inequality is implied by an easier-to-check Bakry-��mery condition depending on the right eigenvector for the sub-Markovian generator, which is not always known. Under additional assumptions on the potential, it is possible to bypass this lack of knowledge showing that exponential quasi-ergodicity is entailed by the classical Bakry-��mery condition. 31 pages |
| Databáze: | OpenAIRE |
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