Rocky Mountain Journal of Mathematics

On the pathwise uniqueness of stochastic partial differential equations with non-Lipschitz coefficients

Defei Zhang and Ping He

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 43, Number 5 (2013), 1739-1746.

First available in Project Euclid: 25 October 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations

Backward doubly stochastic differential equations stochastic partial differential equations pathwise uniqueness non-Lipschitz coefficients


Zhang, Defei; He, Ping. On the pathwise uniqueness of stochastic partial differential equations with non-Lipschitz coefficients. Rocky Mountain J. Math. 43 (2013), no. 5, 1739--1746. doi:10.1216/RMJ-2013-43-5-1739.

Export citation


  • D.A. Dawson, Stochastic evolution equations and related measure-valued processes, J. Multivar. Anal. 5 (1975), 1-52.
  • –––, Measure-valued Markov processes, Écol. Probab. St.-Flour 21, Lect. Notes Math. 1541, Springer, Berlin, 1993.
  • E. Dynkin, Superprocesses and partial differential equations, Ann. Probab. 21 (1993), 1185-1262.
  • E. Dynkin, S.E. Kuznetsov and A.V. Skorokhod, Branching measure-valued processes, Probab. Theor. Rel. Fields 99 (1994), 55-96.
  • J. Lamperti, Continuous state branching processes, Bull. Amer. Math. Soc. 73 (1967), 382-386.
  • X. Mao, Adapted solution of backward stochastic differential equations with non-Lipschitz coefficients, Stoch. Proc. Appl. 58 (1995), 281-292.
  • A. Matoussi and M. Scheutzow, Stochastic PDEs driven by nonlinear noise and backward doubly SDEs, J. Theor. Probab. 15 (2002), 1-39.
  • L. Mytnik, Weak uniqueness for the heat equation with noise, Ann. Probab. 26 (1998), 968-984.
  • L. Mytnik, E. Perkins and A. Sturm, On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients, Ann. Probab. 34 (2006), 1910-1959.
  • E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Syst. Contr. Lett. 14 (1990), 61-74.
  • –––, Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Rel. Fields 98 (1994), 209-227.
  • S. Watanabe, A limit theorem of branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8 (1968), 141-167.
  • J. Xiong, Super-Brownian motion as the unique strong solution to an SPDE, Ann. Probab. 41 (2013), 1030-1054.
  • T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1971), 155-167. \noindentstyle