Backward Stochastic Differential Equations on Manifolds

2005/01/18 by Fabrice Blache, Blache, Fabrice
Mathematics · #FOS: Mathematics #MSC (2000) 58J65 34F05 60G48 #Probability (math.PR) #math.PR #msc:34F05 #msc:58J65 #msc:60G48

paper · pdf · doi:10.48550/arxiv.math/0501265

47 pages To be published in PTRF

arxiv created 2005/01/18 · arxiv updated 2009/12/01

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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