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

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