We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic analysis of Fokker-Planck type equations. We focus on the square integrable framework, and we provide tractable conditions on the infinitesimal generator, including degenerate or anomalously slow diffusions. We take advantage on recent developments in the study of the trend to the equilibrium of ergodic diffusions. We discuss examples and formulate open problems.
Publié le : 2012-07-01
Classification:
Lyapunov criterion,
Markov semigroup,
Markov process,
Functional central limit theorem,
invariance principle,
diffusion process,
long time behavior,
Fokker-Planck equation,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00585271,
author = {Cattiaux, Patrick and Chafai, Djalil and Guillin, Arnaud},
title = {Central limit theorems for additive functionals of ergodic Markov diffusions processes},
journal = {HAL},
volume = {2012},
number = {0},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00585271}
}
Cattiaux, Patrick; Chafai, Djalil; Guillin, Arnaud. Central limit theorems for additive functionals of ergodic Markov diffusions processes. HAL, Tome 2012 (2012) no. 0, . http://gdmltest.u-ga.fr/item/hal-00585271/