  In this paper we generalized static team theory to dynamic team theory, in
the context of stochastic differential decision system with decentralized
noiseless feedback information structures.
  We apply Girsanov's theorem to transformed the initial stochastic dynamic
team problem to an equivalent team problem, under a reference probability
space, with state process and information structures independent of any of the
team decisions. Subsequently, we show, under certain conditions, that
continuous-time and discrete-time stochastic dynamic team problems, can be
transformed to equivalent static team problems, although computing the optimal
team strategies using this method might be computational intensive. Therefore,
we propose an alternative method, by deriving team and Person-by-Person (PbP)
optimality conditions, via the stochastic Pontryagin's maximum principle,
consisting of forward and backward stochastic differential equations, and a set
of conditional variational Hamiltonians with respect to the information
structures of the team members.
  Finally, we relate the backward stochastic differential equation to the value
process of the stochastic team problem.
