Almost sure convergence and stability analysis of hybrid partial differential systems under jump Markovian perturbations (Q2756188)

The authors study almost sure stability properties for solutions of an evolution equation on a bounded domain in \({\mathbb R}^n\) which is randomly perturbed by a finite state Markov process. Using a suitable vector-valued Lyapunov type function, the authors show that the evolution system is almost sure stable (almost sure asymptotically stable or almost sure convergent, respectively) if an associated auxiliary system of linear ODEs exhibits the corresponding stability property.