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Generalized BSDEs and nonlinear Neumann boundary value problems
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  • Published: May 1998

Generalized BSDEs and nonlinear Neumann boundary value problems

  • Etienne Pardoux1 &
  • Shuguang Zhang2 

Probability Theory and Related Fields volume 110, pages 535–558 (1998)Cite this article

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  • 95 Citations

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Summary.

We study a new class of backward stochastic differential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial differential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

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Authors and Affiliations

  1.  Laboratoire d'Analyse, Topologie, Probabilités, CNRS-UMR 6632, Centre de Mathématiques et Informatique, Université de Provence, 39, rue F. Joliot-Curie F-13453 Marseille Cedex 13, France, , , , , , FR

    Etienne Pardoux

  2.  Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui Province, 230026, P.R. China, , , , , , CN

    Shuguang Zhang

Authors
  1. Etienne Pardoux
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  2. Shuguang Zhang
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Received: 27 September 1996 / In revised form: 1 December 1997

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Pardoux, E., Zhang, S. Generalized BSDEs and nonlinear Neumann boundary value problems. Probab Theory Relat Fields 110, 535–558 (1998). https://doi.org/10.1007/s004400050158

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  • Issue Date: May 1998

  • DOI: https://doi.org/10.1007/s004400050158

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  • Mathematics Subject Classification (1991): 60H99
  • 60H30
  • 35J60
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