  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.
