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Existence and uniqueness results for semilinear stochastic partial differential equations

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  • Gyöngy, István

Abstract

We prove existence, uniqueness and comparison theorems for a class of semilinear stochastic partial differential equations driven by space-time white noise. The class of equations we investigate contains as special cases the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise.

Suggested Citation

  • Gyöngy, István, 1998. "Existence and uniqueness results for semilinear stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 271-299, March.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:2:p:271-299
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    Cited by:

    1. Bonnet, Guillaume & Adler, Robert J., 2007. "The Burgers superprocess," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 143-164, February.
    2. Olivera, Christian & Tudor, Ciprian A., 2021. "Absolute continuity of the solution to the stochastic Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Bo, Lijun & Wang, Yongjin, 2011. "On a stochastic interacting model with stepping-stone noises," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1300-1305, August.

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