Backward stochastic differential equations on manifolds

• 成果类型: Article
• 署名作者: Blache, F
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0400-9
• 发表日期: 2005
• 页码: 391-437
• 关键词: harmonic maps; martingales; convexity; probability

摘要

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.