1. Recursive computation of invariant distributions of Feller processes
- Author
-
Clément Rey, Gilles Pagès, Laboratoire de Physique moléculaire et applications (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Statistics and Probability ,Markov chain ,Recursive computation ,Applied Mathematics ,010102 general mathematics ,Markov process ,Stochastic approximation ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Mathematics::Probability ,Modeling and Simulation ,symbols ,Applied mathematics ,Ergodic theory ,Invariant measure ,[MATH]Mathematics [math] ,0101 mathematics ,Invariant (mathematics) ,Brownian motion ,Mathematics - 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 Pages (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.
- Published
- 2020