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Backward doubly stochastic differential equations and systems of quasilinear SPDEs. (English) Zbl 0792.60050
We introduce a new class of backward stochastic differential equations, which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations, thus extending the Feynman-Kac formula for linear SPDE’s.
Reviewer: E.Pardoux

MSC:
60H10Stochastic ordinary differential equations
60H15Stochastic partial differential equations
60H30Applications of stochastic analysis
References:
[1]Krylov, N.V., Rozovskii, B.L.: Stochastic evolution equations. J. Sov. Math.16, 1233-1277 (1981) · Zbl 0462.60060 · doi:10.1007/BF01084893
[2]Nualart, D., Pardoux, E.: Stochastic calculus with anticipating integrands. Probab. Theory Relat. Fields78, 535-581 (1988) · Zbl 0629.60061 · doi:10.1007/BF00353876
[3]Ocone, D., Pardoux, E.: A stochastic Feynman-Kac formula for anticipating SPDEs, and application to nonlinear smoothing. Stochastics45, 79-126 (1993)
[4]Pardoux, E.: Un résultat sur les équations aux dérivés partielles stochastiques et filtrage des processus de diffusion. Note C.R. Acad. Sci., Paris Sér. A287, 1065-1068 (1978)
[5]Pardoux, E.: Stochastic PDEs, and filtering of diffusion processes. Stochastics3, 127-167 (1979)
[6]Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett.14, 55-61 (1990) · Zbl 0692.93064 · doi:10.1016/0167-6911(90)90082-6
[7]Pardoux, E., Peng, S.: Backward stochastic differential equations and quasilinear parabolic partial differential equations. In: Rozuvskii, B.L., Sowers, R.B. (eds.) Stochastic partial differential equations and their applications. (Lect. Notes Control Inf. Sci., vol. 176, pp. 200-217) Berlin Heidelberg New York: Springer 1992
[8]Peng, S.: Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics37, 61-74 (1991)
[9]Peng, S.: A generalized dynamic programming principle and Hamilton-Jacobi-Bellmann equation. Stochastics38, 119-134 (1992)
[10]Peng, S.: A non linear Feynman-Kac formula and applications. In: Chen, S.P., Yong, J.M. (eds.) Proc. of Symposium on system science and control theory, pp. 173-184. Singapore: World Scientific 1992
[11]Rozovskii, B.: Stochastic evolution systems. Dordrecht: Reidel 1991