Quadratic Transportation Cost Inequalities Under Uniform Distance For Stochastic Reaction Diffusion Equations Driven by Multiplicative Space-Time White Noise

In this paper, we established a quadratic transportation cost inequality for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise based on a new inequality we proved for the moments (under the uniform norm) of the stochastic convolution with respect to space-time white noise, which is of independent interest. The solutions of such stochastic partial differential equations are typically not semimartingales on the state space.