  In this paper we propose definitions of equivalence via stochastic
bisimulation and of equivalence of stochastic external behavior for the class
of discrete-time stochastic linear control systems with possibly degenerate
normally distributed disturbances. The first notion is inspired by the notion
of probabilistic bisimulation for probabilistic chains while the second one by
the notion of equivalence of external behavior for (nonstochastic) behavioral
systems. Geometric necessary and sufficient conditions for checking these
notions are derived. Model reduction via Kalman-like decomposition is also
proposed. Connections with stochastic linear realization theory and stochastic
reachability are established.
