Title: A converse Lyapunov theorem for strong global recurrence

Abstract: In this talk we focus on discrete-time stochastic systems
modeled by set-valued mappings. First, we introduce a framework for
generating random processes under certain regularity assumptions for
the system. Next, we discuss a stochastic stability property called
`recurrence'. Sufficient conditions for recurrence in terms of
Lyapunov functions and robustness of recurrence to sufficiently small
state dependent perturbations are established. Lastly, we present a
converse Lyapunov theorem which states that the existence of a smooth
Lyapunov function is a necessary condition for recurrence.