Sufficient sequences and state space models for random processes

Let (U1, U2,...) be a sequence of observed random variables whose probability distributions are described by a parametrized family of density functions {pk(u1,..., Uk; ??)}. If there exists a sequence of sufficient statistics for ??, (T1(U1), T2(U1, U2),...), and if a realizability assumption holds, then there is a finite dimensional state space model whose output process agrees with (U1, U2,...)in distribution.