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Transportation cost-information inequality for non-linear time-fractional stochastic heat equation driven by space–time white noise

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  • Li, Ruinan
  • Li, Yumeng

Abstract

We establish transportation cost-information inequalities T2(C) for solutions of nonlinear stochastic partial differential equation of fractional order in both space and time variables with deterministic and bounded initial conditions: ∂tβu(t,x)+(−Δ)α/2u(t,x)=Itγσ(u(t,x))Ẇ(t,x)in(0,∞)×Rd,where α>0, β∈(0,2], γ≥0, ∂tβ is the Caputo fractional derivative, −(−Δ)α/2 is the fractional/power of Laplacian, Itγ is the Riemann–Liouville integral operator, Ẇ(t,x) is a space–time white noise, and σ:R→R is a bounded and Lipschitz function. Since the space variable is defined on the unbounded domain Rd, the inequalities are proved under a weighted L2-norm in the spatial domain.

Suggested Citation

  • Li, Ruinan & Li, Yumeng, 2026. "Transportation cost-information inequality for non-linear time-fractional stochastic heat equation driven by space–time white noise," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001646
    DOI: 10.1016/j.spl.2025.110519
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    2. Boufoussi, Brahim & Hajji, Salah, 2018. "Transportation inequalities for stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 75-83.
    3. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.
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