Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations

TL;DR

This paper establishes limit theorems and deviation principles for the sample entropy production rate in stochastic differential equations with Lipschitz and dissipative drifts, using advanced probabilistic inequalities.

Contribution

It introduces new asymptotic results for entropy production rates in SDEs, leveraging the dimension-free Harnack inequality and integration by parts techniques.

Findings

Proves the central limit theorem for entropy production rate

Establishes the moderate deviation principle

Derives the logarithmic iteration law

Abstract

By using the dimension-free Harnack inequality and the integration by parts formula for the associated diffusion semigroup, we prove the central limit theorem, the moderate deviation principle, and the logarithmic iteration law for the sample entropy production rate of stochastic differential equations with Lipschitz continuous and dissipative drifts.