Large deviations for diffusions: Donsker-Varadhan meet Freidlin-Wentzell

Abstract

We consider a diffusion process on ${\mathbb{R}}^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the expectation of the Freidlin-Wentzell functional per unit of time. As an application of this result, we obtain a variational representation of the rate function for the Gallavotti-Cohen observable in the small noise and large time limits.

arXiv commentTo appear in Ensaios Matemáticos in a special issue dedicated to Errico Presutti

References in corpus (11)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Dynamical ensembles in stationary states
• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• Entropic fluctuations in thermally driven harmonic networks
• Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations
• Gallavotti-Cohen theorem, Chaotic Hypothesis and the zero-noise limit
• Full metastable asymptotic of the Fisher information
• Small noise asymptotic of the Gallavotti-Cohen functional for diffusion processes
• Metastable $\Gamma$-expansion of finite state Markov chains level two large deviations rate functions
• Metastability from the large deviations point of view: A $\Gamma$-expansion of the level two large deviations rate functional of non-reversible finite-state Markov chains

Cited by in corpus (2)

• Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
• Full $\Gamma$-expansion of reversible Markov chains level two large deviations rate functionals