Fluctuations of the Empirical Measure of Freezing Markov Chains
| Autor: | Bertrand Cloez, Florian Bouguet |
|---|---|
| Přispěvatelé: | Biology, genetics and statistics (BIGS), Inria Nancy - Grand Est, 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), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), 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), Chaire Modelisation Mathematique et Biodiversite, ANR-12-JS01-0006,PIECE,Ergodicité, contrôle et statistique pour les PDMP(2012), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA) |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Mathematical optimization General Mathematics Markov chain 60J10 60J25 60F05 Discrete phase-type distribution Piecewise-deterministic Markov process Long-time behavior 01 natural sciences Mathématiques générales Continuous-time Markov chain 010104 statistics & probability Markov renewal process 60J25 60F05 FOS: Mathematics Statistical physics 0101 mathematics Mathematics Probability Markov chain mixing time convergence 010102 general mathematics Probability (math.PR) long-time behavior piecewise-deterministic Markov process Ornstein-Uhlenbeck process asymptotic pseudotrajectory Probabilités MSC 60J10 Harris chain [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] probabilité Balance equation 60J10 Markov property chaîne de markov Statistics Probability and Uncertainty Mathematics - Probability algorithme Asymptotic pseudotrajectory |
| Zdroj: | Electronic Journal of Probability Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23, pp.1-32. ⟨10.1214/17-EJP130⟩ Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23, ⟨10.1214/17-EJP130⟩ Electronic Journal of Probability (23), 1-32. (2018) Electron. J. Probab. Electronic Journal of Probability, 2018, 23, pp.1-32. ⟨10.1214/17-EJP130⟩ |
| ISSN: | 1083-6489 |
| DOI: | 10.48550/arxiv.1705.02121 |
| Popis: | In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We are interested in the long time behavior of the empirical measure of this freezing Markov chain. Some recent papers provide almost sure convergence and convergence in distribution in the case of the freezing speed $n^{-\theta}$, with different limits depending on $\theta1$. Using stochastic approximation techniques, we generalize these results for any freezing speed, and we obtain a better characterization of the limit distribution as well as rates of convergence as well as functional convergence. Comment: 30 pages |
| Databáze: | OpenAIRE |
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