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In this paper, we established quadratic transportation cost inequalities forsolutions of stochastic reaction diffusion equations driven by multiplicativespace-time white noise on the whole line $\mathbb{R}$. Since the space variableis defined on the unbounded domain $\mathbb{R}$, the inequalities are provedunder a weighted $L^2$-norm and a weighted uniform metric in the so called$L^2_{tem}$, $C_{tem}$ spaces. The new moments estimates of the stochasticconvolution with respect to space-time white noise play an important role. Inaddition, the transportation cost inequalities are also obtained for thestochastic reaction diffusion equations with random initial values.

Transportation cost inequalities for stochastic reaction diffusion equations on the whole line $\mathbb{R}$