English

Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations

Probability 2011-09-06 v1

Abstract

In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs in short) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward backward stochastic differential equations (FBSDEs in short) is established, which can be regarded as an extension of Feynman-Kac formula to non-Markov frame.

Keywords

Cite

@article{arxiv.1109.0672,
  title  = {Semi-linear Degenerate Backward Stochastic Partial Differential Equations and Associated Forward Backward Stochastic Differential Equations},
  author = {Kai Du and Qi Zhang},
  journal= {arXiv preprint arXiv:1109.0672},
  year   = {2011}
}

Comments

23 pages

R2 v1 2026-06-21T18:59:23.189Z