Before revision:  We propose to work in the following procedure: Applying the theory of the monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space.
After revision:  We propose to work in the following procedure: Applying the theory of monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space.