This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependent and random coefficients. As opposed to the {deterministic} path-dependent cases, the value function turns out to be a random field on the path spaces and it is characterized with a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.
Optimal control of infinite-dimensional differential systems with randomness and path-dependence and stochastic path-dependent Hamilton-Jacobi equations
Duality for Nonlinear Filtering II: Optimal Control
Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems
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