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Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs

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  • Anis Matoussi

    (Technische Universität Berlin)

  • Michael Scheutzow

Abstract

We study a “new kind” of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space-time noise.

Suggested Citation

  • Anis Matoussi & Michael Scheutzow, 2002. "Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs," Journal of Theoretical Probability, Springer, vol. 15(1), pages 1-39, January.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:1:d:10.1023_a:1013803104760
    DOI: 10.1023/A:1013803104760
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Hu, Ying, 1993. "Probabilistic interpretation of a system of quasilinear elliptic partial differential equations under Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 107-121, October.
    3. V. Bally & A. Matoussi, 2001. "Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 14(1), pages 125-164, January.
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    Cited by:

    1. Hu, Yaozhong & Li, Juan & Mi, Chao, 2023. "BSDEs generated by fractional space-time noise and related SPDEs," Applied Mathematics and Computation, Elsevier, vol. 450(C).

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