Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise

2019/10/11 by Shijie Shang, Ran Wang, shang, Shijie +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60E15 #60H15 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1910.04934

openalex publication_date 2019/10/11 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of solution to a stochastic heat equation defined on [0,T]× [0,1]^d. This equation is driven by the Gaussian noise, white in time and colored in space. The proof is based on a new moment inequality under the uniform metric for the stochastic convolution with respect to the time-white and space-colored noise, which is of independent interest.

Citations

• Talagrand Inequality on Free Path Space and Application to Stochastic Reaction Diffusion Equations

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• Transportation cost inequalities for singular SPDEs

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