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Central limit theorems for additive functionals of ergodic Markov diffusions processes

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00585271
Contributor : Arnaud Guillin <>
Submitted on : Tuesday, April 12, 2011 - 2:02:55 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Wednesday, July 13, 2011 - 2:40:56 AM

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  • HAL Id : hal-00585271, version 1
  • ARXIV : 1104.2198

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Patrick Cattiaux, Djalil Chafai, Arnaud Guillin. Central limit theorems for additive functionals of ergodic Markov diffusions processes. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2012, 9 (2), pp.337-382. ⟨hal-00585271⟩

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