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

Abstract

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 $L_{tem}^2$, $C_{tem}$ 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.

References in corpus (3)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion
• A new characterization of Talagrand's transport-entropy inequalities and applications