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On non-degenerate quasi-linear stochastic partial differential equations

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Abstract

We prove a limit theorem for non-degenerate quasi-linear parabolic SPDEs driven by space-time white noise in one space-dimension, when the diffusion coefficient is Lipschitz continuous and the nonlinear drift term is only measurable. Hence we obtain an existence and uniqueness and a comparison theorem, which generalize those in [2], [4], [5] to the case of non-degenerate SPDEs with measurable drift and Lipschitz continuous diffusion coefficients.

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Authors and Affiliations

  1. Department of Probability and Statistics, Eötvös Loránd University Budapest, Múzeum krt. 6-8, 1088, Hungary

    István Gyöngy

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  1. István Gyöngy
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Research supported by the Hungarian National Foundation of Scientific Research No. 2290.

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Gyöngy, I. On non-degenerate quasi-linear stochastic partial differential equations. Potential Anal 4, 157–171 (1995). https://doi.org/10.1007/BF01275588

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  • DOI: https://doi.org/10.1007/BF01275588

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