  Recently, there have been efforts towards understanding the sampling
behaviour of event-triggered control (ETC), for obtaining metrics on its
sampling performance and predicting its sampling patterns. Finite-state
abstractions, capturing the sampling behaviour of ETC systems, have proven
promising in this respect. So far, such abstractions have been constructed for
non-stochastic systems. Here, inspired by this framework, we abstract the
sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC)
systems via Interval Markov Chains (IMCs). Particularly, we define functions
over sequences of state-measurements and interevent times that can be expressed
as discounted cumulative sums of rewards, and compute bounds on their expected
values by constructing appropriate IMCs and equipping them with suitable
rewards. Finally, we argue that our results are extendable to more general
forms of functions, thus providing a generic framework to define and study
various ETC sampling indicators.
