Spectral stability of Markov systems

Abstract

For a class of semigroups of stochastic dynamical systems, $x\mapsto P_x$, where $x$ denotes a state and $P_x$ the state probability transition, we relate its spectral stability with the combinatorial stability of the underlying non-deterministic dynamics, associated to the point-set map $x\mapsto \text{ supp}(P_x)$.