In this paper, we established quadratic transportation cost inequalities for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise on the whole line $\mathbb{ R}$. Since the space variable is defined on the unbounded domain $\mathbb{ R}$, the inequalities are proved under 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 stochastic convolution with respect to space-time white noise play an important role. In addition, the transportation cost inequalities are also obtained for the stochastic reaction diffusion equations with random initial values.
Categories: math.PR