Probability Theory and Related Fields

, Volume 98, Issue 2, pp 209–227

Backward doubly stochastic differential equations and systems of quasilinear SPDEs

  • Etienne Pardoux
  • Shige Peng

DOI: 10.1007/BF01192514

Cite this article as:
Pardoux, E. & Peng, S. Probab. Th. Rel. Fields (1994) 98: 209. doi:10.1007/BF01192514


We introduce a new class of backward stochastic differential equations, which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations, thus extending the Feynman-Kac formula for linear SPDE's.

Mathematics Subject Classification


Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Etienne Pardoux
    • 1
  • Shige Peng
    • 2
  1. 1.Laboratoire APT, URA 225Université de ProvenceMarseille Cedex 3France
  2. 2.Institute of MathematicsShandong UniversityJinanPeople's Republic of China