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A probabilistic interpretation of the divergence and BSDE's

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  • Stoica, I. L.

Abstract

We prove a stochastic representation, similar to the Feynman-Kac formula, for solutions of parabolic equations involving a distribution expressed as divergence of a measurable field. This leads to an extension of the method of backward stochastic differential equations to a class of nonlinearities larger than the usual one.

Suggested Citation

  • Stoica, I. L., 2003. "A probabilistic interpretation of the divergence and BSDE's," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 31-55, January.
    • Handle: RePEc:eee:spapps:v:103:y:2003:i:1:p:31-55
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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. Rozkosz, Andrzej, 1996. "Stochastic representation of diffusions corresponding to divergence form operators," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 11-33, October.
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    Cited by:

    1. Matoussi, A. & Piozin, L. & Popier, A., 2017. "Stochastic partial differential equations with singular terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 831-876.
    2. Lejay, Antoine, 2004. "A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 145-176, March.
    3. Liu, Xuan & Qian, Zhongmin, 2018. "Backward problems for stochastic differential equations on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3387-3418.

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