On stochastic observability and controllability

New definitions of stochastic observability, detectability, controllability and reachability are proposed. For both continuous and discrete time linear systems easily verifiable necessary and sufficient conditions are obtained, which are compatible with the usual ones for the corresponding (degenerate) deterministic systems. Furthermore, for stochastically observable, linear systems explicit expressions for the LUMCE of the state at time $\text{t≧0}$, with no information of the initial state, are obtained.