Model reduction of continuous-time stochastic linear control systems via bisimulation equivalence

In this paper we consider continuous-time stochastic linear control systems and propose model reduction techniques which are based on the notion of equivalence via stochastic bisimulation. Starting from our earlier work on equivalences given for discrete-time stochastic control systems we first extend the notion of stochastic bisimulation equivalence and the corresponding geometric conditions to the present framework. We then define the quotient linear systems induced by the equivalence notion and show that the obtained system is equivalent via stochastic bisimulation to the original one. We finally discuss model reduction to the system with minimal dimension in the state space.