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Backward stochastic differential equations on manifolds
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  • Published: 27 December 2004

Backward stochastic differential equations on manifolds

  • Fabrice Blache1 

Probability Theory and Related Fields volume 132, pages 391–437 (2005)Cite this article

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Abstract.

The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problems on manifolds.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Blaise Pascal, 63177, Aubière Cedex, France

    Fabrice Blache

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  1. Fabrice Blache
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Blache, F. Backward stochastic differential equations on manifolds. Probab. Theory Relat. Fields 132, 391–437 (2005). https://doi.org/10.1007/s00440-004-0400-9

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  • Received: 11 December 2003

  • Published: 27 December 2004

  • Issue Date: July 2005

  • DOI: https://doi.org/10.1007/s00440-004-0400-9

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Keywords

  • Differential Equation
  • Manifold
  • Stochastic Process
  • Probability Theory
  • Differential Geometry
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