Acta Mathematica Scientia

, Volume 39, Issue 3, pp 857–873 | Cite as

Uniqueness of Viscosity Solutions of Stochastic Hamilton-Jacobi Equations

  • Jinniao QiuEmail author
  • Wenning WeiEmail author


This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the associated stochastic HJ equation.

Key words

Stochastic Hamilton-Jacobi equation optimal stochastic control backward stochastic partial differential equation viscosity solution 

2010 MR Subject Classification

49L20 49L25 93E20 35D40 60H15 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of CalgaryCalgaryCanada

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