Team Optimality Conditions of Distributed Stochastic Differential Decision Systems With Decentralized Noisy Information Structures

A team problem formulation of distributed stochastic differential systems with decentralized noisy information structures is considered, and a stochastic Pontryagin's maximum principle is applied to derive sufficient team and person-by-person optimality conditions. The sufficient conditions are given in terms of local convexity conditions of the Hamiltonian, and the corresponding conditional variational equations. These appear to be analogous to the convexity of the pay-off, in the action spaces, of static team problems. The stochastic maximum principle is applied to several examples in filtering and control.