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