The Measurable Space of Stochastic Processes

We introduce a stochastic extension of CCS endowed with structural operational semantics expressed in terms of measure theory. The set of processes is organised as a measurable space by the sigma-algebra generated by structural congruence. The structural operational semantics associates to each process a set of measures over the space of processes. The measures encode the rates of the transitions from a process state of a system to a measurable set of processes. We prove that the stochastic bisimilarity is a congruence, which extends the structural congruence. In addition to an elegant operational semantics, our calculus provides a canonic way to define metrics on processes that measure how similar two processes are in terms of behaviour.

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