Talagrand Concentration Inequalities for Stochastic Partial Differential Equations

Abstract

One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.

19 pages. Keywords: Stochastic partial differential equations, stochastic heat equation, stochastic fractional heat equation, concentration of measure, transportation-information inequality, relative entropy, Wasserstein distance