On a recurrence principle for a class of stochastic hybrid systems

For a class of stochastic hybrid systems, we characterize the sets to which bounded solutions converge. We show that each sample path converges to a weakly totally recurrent in probability set. This characterization is often tighter than the usual assertion that a solution converges to a weakly invariant set. Consequently, the results here can be viewed as a generalization of the invariance principle, to a broad class of stochastic hybrid systems that admit non-unique solutions.