Talagrand’s quadratic transportation cost inequalities for reflected SPDEs driven by space–time white noise

Abstract

Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for laws of the solutions of reflected SPDEs under the uniform norm on the continuous path space. These equations are driven by space–time white noise with deterministic or random initial values. The proofs are heavily based on the methods of Shang and Zhang (2019) and Wu and Zhang (2014).