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Talagrand’s quadratic transportation cost inequalities for reflected SPDEs driven by space–time white noise

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  • Li, Ruinan
  • Li, Yumeng

Abstract

Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for laws of the solutions of reflected SPDEs under the uniform norm on the continuous path space. These equations are driven by space–time white noise with deterministic or random initial values. The proofs are heavily based on the methods of Shang and Zhang (2019) and Wu and Zhang (2014).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300377
    DOI: 10.1016/j.spl.2020.108734
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    References listed on IDEAS

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    1. Boufoussi, Brahim & Hajji, Salah, 2018. "Transportation inequalities for stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 75-83.
    2. 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.
    3. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    Cited by:

    1. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    2. Li, Ruinan & Zhang, Beibei, 2024. "A transportation inequality for reflected SPDEs on infinite spatial domain," Statistics & Probability Letters, Elsevier, vol. 206(C).

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