Fisher information bounds and applications to SDEs with small noise

TL;DR

This paper derives bounds on Fisher information for Malliavin differentiable variables and analyzes the convergence rate to normality in small noise SDEs, demonstrating optimal order results.

Contribution

It establishes general Fisher information bounds and characterizes the optimal convergence rate in the CLT for small noise SDE solutions.

Findings

Fisher information bounds for Malliavin differentiable variables

Optimal convergence rate in the CLT for small noise SDEs

Application to additive functionals of SDE solutions

Abstract

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central limit theorem for the solution of small noise stochastic differential equations and its additive functionals. We also show that the convergence rate is of optimal order.