Central limit theorems for additive functionals of ergodic Markov diffusions processes

摘要

We revisit functional central limit theorems for additive functionals ofergodic Markov diffusion processes. Translated in the language of partialdifferential equations of evolution, they appear as diffusion limits in theasymptotic analysis of Fokker-Planck type equations. We focus on the squareintegrable framework, and we provide tractable conditions on the infinitesimalgenerator, including degenerate or anomalously slow diffusions. We takeadvantage on recent developments in the study of the trend to the equilibriumof ergodic diffusions. We discuss examples and formulate open problems.