Stability of hybrid linear stochastic systems - a technical tool in recursive identification

The identification of continuous-time stochastic systems, in particular recursive estimation, is a basic building block for continuous-time stochastic adaptive filtering and control as well, see the works of Van Schuppen, Duncan and Pasik-Duncan. In these papers the underlying stochastic systems is essentially an AR-system, for which the recursive maximum-likelihood (RML) estimation reduces to a recursive least squares (RLSQ) estimation. Recursive estimation in the same generality has been studied by DeWolf and Wiberg, under the condition that the process is stopped if it reached the boundary of a truncation domain. A rigorous convergence theory for a restricted class of non-linear stochastic systems has been given by Levanony and Zeitouini for explicit systems.