Exponential Convergence for Functional SDEs with H\"older Continuous Drift

TL;DR

This paper proves exponential convergence in Wasserstein distance, entropy, and total variation for a class of functional SDEs with H"older continuous drift using Zvonkin's transform and related inequalities.

Contribution

It establishes the first exponential convergence results for such SDEs with H"older continuous drift, combining Zvonkin's transform with functional inequalities.

Findings

Exponential convergence in Wasserstein distance.

Convergence in entropy and total variation norms.

Application of Zvonkin's transform to functional SDEs.

Abstract

Applying Zvonkin's transform, the exponential convergence in Wasserstein distance for a class of functional SDEs with H\"older continuous drift is obtained. This combining with log-Harnack inequality implies the same convergence in the sense of entropy, which also yields the convergence in total variation norm by Pinsker's inequality.