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A transportation inequality for reflected SPDEs on infinite spatial domain

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  • Li, Ruinan
  • Zhang, Beibei

Abstract

For the stochastic partial differential equation with reflection on the infinite spatial domain, we establish a quadratic transportation cost inequality under the weighted sup-norm. The proof is based on a new moment inequality under the weighted sup-norm for the stochastic convolution with respect to the space–time white noise.

Suggested Citation

  • Li, Ruinan & Zhang, Beibei, 2024. "A transportation inequality for reflected SPDEs on infinite spatial domain," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223001839
    DOI: 10.1016/j.spl.2023.109959
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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. Li, Ruinan & Li, Yumeng, 2020. "Talagrand’s quadratic transportation cost inequalities for reflected SPDEs driven by space–time white noise," Statistics & Probability Letters, Elsevier, vol. 161(C).
    3. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
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