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On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise

Author

Listed:
  • Zhang, Bin
  • Yao, Zhigang
  • Liu, Junfeng

Abstract

In this paper, we study a class of nonlinear stochastic heat equations ∂∂tu(t,x)=Δ+aαΔα2+b⋅∇u(t,x)+σ(u(t,x))Ẇ(t,x), where Ẇ denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.

Suggested Citation

  • Zhang, Bin & Yao, Zhigang & Liu, Junfeng, 2023. "On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise," Statistics & Probability Letters, Elsevier, vol. 196(C).
  • Handle: RePEc:eee:stapro:v:196:y:2023:i:c:s0167715223000317
    DOI: 10.1016/j.spl.2023.109807
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Jian, 2013. "A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1083-1103.
    2. Raluca M. Balan & Ciprian A. Tudor, 2010. "Stochastic Heat Equation with Multiplicative Fractional-Colored Noise," Journal of Theoretical Probability, Springer, vol. 23(3), pages 834-870, September.
    3. Chen, Zhen-Qing & Hu, Eryan, 2015. "Heat kernel estimates for Δ+Δα/2 under gradient perturbation," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2603-2642.
    4. Junfeng Liu & Litan Yan, 2016. "Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise," Journal of Theoretical Probability, Springer, vol. 29(1), pages 307-347, March.
    Full references (including those not matched with items on IDEAS)

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