Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton–Jacobi equations

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed deterministic path-dependent cases, value function turns out be a random field on path space it characterized by Hamilton–Jacobi (SPHJ) equation. A notion viscosity solution proposed proved unique associated SPHJ