On infinite-horizon probabilistic properties and stochastic bisimulation functions

This work investigates infinite-horizon properties over discrete-time stochastic models with continuous state spaces. The focus is on understanding how the structural features of a model (e.g., the presence of absorbing sets) affect the values of these properties and relate to their uniqueness. Furthermore, we argue that the investigation of these features can lead to approximation bounds for the value of such properties, as well as to improvements on their computation. The article employs the presented results to find a stochastic bisimulation function of two processes.