  Different stochastic extensions of hybrid automata have been proposed in the
past, with unclear expressivity relations between them. To structure and relate
these modeling languages, in this paper we formalize two alternative approaches
to extend hybrid automata with stochastic choices of discrete events and their
time points. The first approach, which we call decomposed scheduling, adds
stochasticity via stochastic races, choosing random time points for the
possible discrete events and executing a winner with an earliest time. In
contrast, composed scheduling first samples the time point of the next event
and then the event to be executed at the sampled time point. We relate the two
approaches regarding their expressivity and categorize available stochastic
extensions of hybrid automata from the literature.
