Transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by space-time white noise

2026/07/19 by Shijie Shang, Tusheng Zhang
#math.PR

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Abstract

In this paper, we establish transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by multiplicative space-time white noise. In particular, the transportation-cost inequalities are established with respect to the L¹ metric, the L² metric and the uniform metric under different dissipativity strengths of the drift. We first obtain a global-in-time and spatially uniform moment estimate for stochastic convolutions driven by space-time white noise, which is of independent interest. We then establish Lipschitz continuity of the solutions to the associated stochastic controlled equations with respect to the controls with a time-independent Lipschitz constant. Applying this Lipschitz continuity estimate, we finally prove transportation-cost inequalities for the invariant measures of stochastic reaction-diffusion equations.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

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