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In this article, a notion of viscosity solutions is introduced for secondorder path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated withoptimal control problems for path-dependent stochastic evolution equations inHilbert spaces. We identify the value functional of optimal control problems asunique viscosity solution to the associated PHJB equations. We also show thatour notion of viscosity solutions is consistent with the corresponding notionof classical solutions, and satisfies a stability property.

Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Spaces