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dt+Z\\left(t\\right) dW\\left(t\\right),\\;0\\leq t\\leq T,\\medskip\\\\ \\multicolumn{1}{l}{Y\\left(T\\right) =\\xi,}\\end{array} \\right. \\] where $\\partial\\varphi$ is the subdifferential of a convex function and $\\left(Y_{t},Z_{t}\\right):=(Y(t+\\theta),Z(t+\\theta))_{\\theta\\in\\lbrack-T,0]}$ represent the past values of the solution over the interval 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