  In this article, a notion of viscosity solutions is introduced for second
order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with
optimal control problems for path-dependent stochastic differential equations.
We identify the value functional of optimal control problems as unique
viscosity solution to the associated PHJB equations. We also show that our
notion of viscosity solutions is consistent with the corresponding notion of
classical solutions, and satisfies a stability property. Applications to
backward stochastic Hamilton-Jacobi-Bellman equations are also given.
