On Forward Backward Stochastic Differential Equations with Random Coefficients

  • 报告人: 尹宏教授State University of New York
  • 报告地址: 长江数学中心409
  • 报告时间: 2016年12月29日 16:00-17:00
  • 主题摘要:
 The main purpose of this talk is to establish an equivalence relationship between well-posedness of forward backward stochastic differential equations (FBSDEs) with random coefficients and that of backward stochastic PDEs. For FBSDEs with deterministic coefficients, it is well-known that the backward component of the FBSDEs can be written as a deterministic function of the forward component, and this function is the solution to a PDE in certain weak sense. For general FBSDEs, such function becomes a random field and the corresponding PDE becomes a backward SPDE. We show that, under certain conditions, the FBSDEs is well-posed if and only if this random field is a Sobolev type weak solution to the BSPDE. This result extends the well-known four step scheme to a random coefficients case, and provides a Feynman-Kac type formula for solutions to BSPDEs. As a corollary, we prove the well-posedness and comparison principle for quasilinear BSPDEs, which is also novel in the literature.