UNIQUENESS OF VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI EQUATIONS

doi:10.1007/s10473-019-0314-3

Abstract

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.

Key words: Stochastic Hamilton-Jacobi equation, optimal stochastic control, backward stochastic partial differential equation, viscosity solution

CLC Number:

49L20

Jinniao QIU, Wenning WEI. UNIQUENESS OF VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI EQUATIONS[J].Acta mathematica scientia,Series B, 2019, 39(3): 857-873.

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