Transportation cost inequalities for diffusions under uniform distance

TL;DR

This paper establishes transportation inequalities for the laws of diffusion processes under the uniform norm, particularly for those with Lipschitz or dissipative coefficients, and applies these results to certain singular stochastic differential equations.

Contribution

It introduces transportation inequalities under the uniform norm for diffusion processes with specific coefficient conditions and applies these to singular stochastic differential equations.

Findings

Proved transportation inequalities for diffusions with Lipschitz/dissipative coefficients.

Applied inequalities to singular stochastic differential equations.

Extended the scope of transportation inequalities to uniform norms.

Abstract

We prove the transportation inequality with the uniform norm for the laws of diffusion processes with Lipschitz and/or dissipative coefficients and apply them to some singular stochastic differential equations of interest.