# State and Control Paths-Dependent Stochastic Zero-Sum Differential Games: Dynamic Programming Principle and Viscosity Solution of Paths-Dependent Hamilton-Jacobi-Isaacs Equation.

@inproceedings{Moon2019StateAC, title={State and Control Paths-Dependent Stochastic Zero-Sum Differential Games: Dynamic Programming Principle and Viscosity Solution of Paths-Dependent Hamilton-Jacobi-Isaacs Equation.}, author={Jun Hyuk Moon}, year={2019} }

In this paper, we consider state and control paths-dependent stochastic zero-sum differential games, where the dynamics and the running cost include both the state and control paths of the players. Using the notion of nonanticipative strategies, we define lower and upper value functionals, which are functions of the initial state and control paths of the players. We prove that the value functionals satisfy the dynamic programming principle. The associated lower and upper Hamilton-Jacobi-Isaacs… CONTINUE READING

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