Abstract
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.
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**niao Qiu is partially supported by the National Science and Engineering Research Council of Canada (NSERC) and by the start-up funds from the University of Calgary. The support of the NSERC grant of Professor Robert Elliott for Wenning Wei is gratefully acknowledged.
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Qiu, J., Wei, W. Uniqueness of Viscosity Solutions of Stochastic Hamilton-Jacobi Equations. Acta Math Sci 39, 857–873 (2019). https://doi.org/10.1007/s10473-019-0314-3
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DOI: https://doi.org/10.1007/s10473-019-0314-3
Key words
- Stochastic Hamilton-Jacobi equation
- optimal stochastic control
- backward stochastic partial differential equation
- viscosity solution