By a memory mean-field process we mean the solution X() of a stochastic mean-field equation involving not just the current state X(t) and its law L(X(t)) at time t, but also the state values X(s) and its law L(X(s)) at some previous times s

Keywords:Mean-field stochastic differential equation;Law process;Memory;Path segment spaces;Random probability measures;Stochastic maximum principle;Operator-valued absde;Mean-variance problem