Dynamic team optimality conditions of distributed stochastic differential decision systems with decentralized noisy information structures

We derive team and Person-by-Person (PbP) optimality conditions using the stochastic Pontryagin´s maximum principle, for distributed stochastic differential decision systems with decentralized noisy information structures. The optimality conditions are given by a Hamiltonian system consisting of forward and backward stochastic differential equations, and conditional Hamiltonians. We also show that, under global convexity conditions, PbP optimality implies team optimality. Finally, we apply the stochastic maximum principle to examples from communications, filtering and control.