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Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise

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  • Gyöngy, István
  • Nualart, David

Abstract

In this paper we consider an implicit approximation scheme for the heat equation with a nonlinear term and an additive space-time white noise. Assuming that the nonlinear drift is measurable and verifies a one-sided linear growth condition we show that the approximation scheme converges to the unique solution in probability, uniformly in space and time.

Suggested Citation

  • Gyöngy, István & Nualart, David, 1995. "Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 57-72, July.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:1:p:57-72
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    Cited by:

    1. Millet, Annie & Morien, Pierre-Luc, 2005. "On implicit and explicit discretization schemes for parabolic SPDEs in any dimension," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1073-1106, July.

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