Stochastic Analysis via a Probabilistic Process Algebra

We propose a probabilistic process algebra built on top of a fully parallel calculus. Being strongly inspired by LOTOS, our model allows for multi-party synchronization in process parallel composition. Anyway, departing from LOTOS, it has a non-interleaving, multiset, semantics: Independent actions are performed simultaneously, whereas synchronization is achieved by means of the minimal, implicit, delay needed for it to take place. In the terminology usually adopted for probabilistic calculi, the process algebra we present is somehow in between the generative and the stratiied ones in that it catches the main features of both. In the paper much of the focus is on the application of the Markov theory to the probabilistic transition systems which result from the expressions of the process algebra. By a detailed example of a simple monitoring and control system, we show how the calculus can be used for specifying and reasoning about stochastic behaviour. Also, we sketch a general procedure for reducing the size of Markov systems in order to simplify linear algebra computations.