Stochastic approximation of quasi-stationary distributions on compact spaces and applications
| Autor: | Bertrand Cloez, Michel Benaïm, Fabien Panloup |
|---|---|
| Přispěvatelé: | Institut de Mathématiques (UNINE), Université de Neuchâtel (UNINE), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), PANORisk, Institut de Mathematiques, SNF : 200020/149871, 200021/175728 |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
reinforced random walks random perturba- tions of dynamical systems Euler scheme Quasi-stationary distributions Boundary (topology) Markov process Stochastic approximation 01 natural sciences Measure (mathematics) 010104 statistics & probability symbols.namesake Position (vector) stochastic approximation spectral gap Secondary 34F05 FOS: Mathematics random perturba-tions of dynamical systems Applied mathematics 0101 mathematics 60J20 Mathematics 60J60 Euler scheme AMS-MSC 65C20 Markov chain 010102 general mathematics Probability (math.PR) random perturbations of dynamical systems [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Compact space 34F05 symbols 60J10 Spectral gap 65C20 Statistics Probability and Uncertainty extinction rate 60B12 Mathematics - Probability |
| Zdroj: | Annals of Applied Probability Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2018, 28 (4), pp.2370-2416 Ann. Appl. Probab. 28, no. 4 (2018), 2370-2416 Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2018, 28 (4), pp.2370-2416. ⟨10.1214/17-AAP1360⟩ |
| ISSN: | 1050-5164 2168-8737 |
| DOI: | 10.1214/17-AAP1360⟩ |
| Popis: | International audience; In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ensuring the convergence of this measure to the quasi-stationary distribution of the chain. We then apply this method to the numerical approximation of the quasi-stationary distribution of a diffusion process killed on the boundary of a compact set and to the estimation of the spectral gap of irreducible Markov processes. Finally, the sharpness of the assumptions is illustrated through the study of the algorithm in a non-irreducible setting. |
| Databáze: | OpenAIRE |
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