Talagrand’s transportation inequality for SPDEs with locally monotone drifts

Ruinan Li and Xinyu Wang

Statistics & Probability Letters, 2024, vol. 204, issue C

Abstract: The purpose of this paper is twofold. Firstly, we prove transportation inequalities T2(C) on the space of continuous paths with respect to the uniform metric for the law of the solution to a class of non-linear monotone stochastic partial differential equations (SPDEs) driven by the Wiener noise. Furthermore, we also establish the T1(C) property for such SPDEs but with merely locally monotone coefficients, including the stochastic Burgers type equation and stochastic 2-D Navier–Stokes equation.

Keywords: Stochastic partial differential equation; Transportation inequality; Locally monotone; Girsanov transformation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.109945

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