Continuous time and/or continuous distributions

Abstract

We compare two models of processes involving uncountable space. Labelled Markov processes are probabilistic transition systems that can have uncountably many states, but still make discrete time steps. The probability measures on the state space may have uncountable support. Hybrid processes are a combination of a continuous space process that evolves continuously with time and of a discrete component, such as a controller. Existing extensions of Hybrid processes with probability restrict the probabilistic behavior to the discrete component. We use an example of an aircraft to highlight the differences between the two models and we define a generalization of both that can model all the features of our aircraft example. © 2010 Springer-Verlag.