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Recursive computation of invariant distributions of Feller processes

Institution:	1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy;2. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy;1. Université Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France;2. Université de Paris, Laboratoire de Probabilités, Statistique et Modélisation (LPSM), F-75013 Paris, France;1. College of Mathematics, Jilin University, Changchun 130012, PR China;2. College of Computer Science and Technology, Jilin University, Changchun 130012, PR China;3. School of Mathematics and statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, PR China;1. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Abstract:	This paper provides a general and abstract approach to compute invariant distributions for Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton and Pagès (2002) and based on simulation algorithms of stochastic schemes with decreasing steps can be used to build invariant measures for general Feller processes. We also propose various applications: Approximation of Markov Brownian diffusion stationary regimes with a Milstein or an Euler scheme and approximation of a Markov switching Brownian diffusion stationary regimes using an Euler scheme.

Keywords:	Ergodic theory Markov process Invariant measure Limit theorem Stochastic approximation
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