Exponential convergence for functional SDEs with Hölder continuous drift

Abstract

Applying Zvonkin’s transform, the exponential convergence in Wasserstein distance for a class of functional SDEs with Hölder 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.

Keywords:

• Functional SDEs
• Zvonkin’s transform
• Hölder continuity
• exponential convergence
• Wasserstein distance

AMS SUBJECT CLASSIFICATION:

• 60H10
• 60B10

Acknowledgements

The author would like to thank Professor Feng-Yu Wang and Shao-Qin Zhang for helpful comments.

Additional information

Funding

Supported in part by NNSFC (11801406). National Natural Science Foundation of China.