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Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

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  • Nualart, David
  • Quer-Sardanyons, Lluís

Abstract

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in (d>=1 and d

Suggested Citation

  • Nualart, David & Quer-Sardanyons, Lluís, 2009. "Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3914-3938, November.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3914-3938
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    References listed on IDEAS

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    1. Márquez-Carreras, D. & Mellouk, M. & Sarrà, M., 2001. "On stochastic partial differential equations with spatially correlated noise: smoothness of the law," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 269-284, June.
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    Cited by:

    1. Hildebrandt, Florian & Trabs, Mathias, 2023. "Nonparametric calibration for stochastic reaction–diffusion equations based on discrete observations," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 171-217.
    2. 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.

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