Uniform convergence of penalized time-inhomogeneous Markov processes
| Autor: | Nicolas Champagnat, Denis Villemonais |
|---|---|
| Přispěvatelé: | TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
uniform exponential mixing Statistics::Theory Uniform convergence Markov process one-dimensional diffusions with absorption 01 natural sciences time-inhomogeneous Markov processes Statistics::Machine Learning 010104 statistics & probability symbols.namesake Exponential stability Dobrushin's ergodic coefficient FOS: Mathematics Statistics::Methodology Applied mathematics 0101 mathematics Contraction (operator theory) Mathematics asymptotic stability 010102 general mathematics Probability (math.PR) penalized processes Feynman–Kac formula Probability and statistics Feynman-Kac formula birth and death processes in random environment with killing Birth–death process Statistics::Computation Exponential function MSC: Primary: 60B10 60F99 60J57 37A25. Secondary: 60J60 60J27 [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] symbols Mathematics - Probability |
| Zdroj: | ESAIM: Probability and Statistics ESAIM: Probability and Statistics, 2018, 22, pp.129-162. ⟨10.1051/ps/2017022⟩ ESAIM: Probability and Statistics, EDP Sciences, 2018, 22, pp.129-162. ⟨10.1051/ps/2017022⟩ |
| ISSN: | 1292-8100 1262-3318 |
| DOI: | 10.1051/ps/2017022⟩ |
| Popis: | We provide a general criterion ensuring the exponential contraction of Feynman–Kac semi-groups of penalized processes. This criterion applies to time-inhomogeneous Markov processes with absorption and killing through penalization. We also give the asymptotic behavior of the expected penalization and provide results of convergence in total variation of the process penalized up to infinite time. For exponential convergence of penalized semi-groups with bounded penalization, a converse result is obtained, showing that our criterion is sharp in this case. Several cases are studied: we first show how our criterion can be simply checked for processes with bounded penalization, and we then study in detail more delicate examples, including one-dimensional diffusion processes conditioned not to hit 0 and penalized birth and death processes evolving in a quenched random environment. |
| Databáze: | OpenAIRE |
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