  In this paper, we present a complete stochastic realization theory for
stochastic jump-linear systems. We present necessary and sufficient conditions
for the existence of a realization, along with a characterization of minimality
in terms of reachability and observability. We also formulate a realization
algorithm and argue that minimality can be checked algorithmically. The main
tool for solving the stochastic realization problem for jump-linear systems is
the formulation and solution of a stochastic realization problem for a general
class of bilinear systems with non-white-noise inputs. The solution to this
generalized stochastic bilinear realization problem is based on the theory of
formal power series. Stochastic jump-linear systems represent a special case of
generalized stochastic bilinear systems.
