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Talagrand’s transportation inequality for SPDEs with locally monotone drifts

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  • Li, Ruinan
  • Wang, Xinyu

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.

Suggested Citation

  • Li, Ruinan & Wang, Xinyu, 2024. "Talagrand’s transportation inequality for SPDEs with locally monotone drifts," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001694
    DOI: 10.1016/j.spl.2023.109945
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    References listed on IDEAS

    as
    1. Boufoussi, Brahim & Hajji, Salah, 2018. "Transportation inequalities for stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 75-83.
    2. Daniel Lacker, 2018. "Liquidity, Risk Measures, and Concentration of Measure," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 813-837, August.
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