Uniqueness of Viscosity Solutions of Stochastic Hamilton-Jacobi Equations
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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 wordsStochastic Hamilton-Jacobi equation optimal stochastic control backward stochastic partial differential equation viscosity solution
2010 MR Subject Classification49L20 49L25 93E20 35D40 60H15
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- Buckdahn R, Keller C, Ma J, Zhang J. Pathwise viscosity solutions of stochastic PDEs and forward path-dependent PDEs—a rough path view. arXiv:1501.06978, 2015Google Scholar
- Pardoux E. Stochastic partial differential equations and filtering of diffusion processes. Stoch, 1979: 127–167Google Scholar
- Peng S. Backward stochastic differential equation, nonlinear expectation and their applications. Proceedings of the International Congress of Mathematicians, 2010: 393–432Google Scholar
- Peng S. Note on viscosity solution of path-dependent PDE and G-martingales. arXiv:1106.1144, 2011Google Scholar