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[CSKN05] S. Cattani, R. Segala, M. Kwiatkowska and G. Norman. Stochastic transition systems for continuous state spaces and non-determinism. In V. Sassone (editor), Proc. Foundations of Software Science and Computation Structures (FOSSACS'05), volume 3441 of Lecture Notes in Computer Science, pages 125-139, Springer Verlag. April 2005. [ps.gz] [pdf] [bib]
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Abstract. We study the interaction between non-deterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been introduced previously. Here, we introduce a model that extends probabilistic automata to the continuous setting. We identify the class of schedulers that ensures measurability properties on executions, and show that such measurability properties are preserved by parallel composition. Finally, we show how these results allow us to define an alternative notion of weak bisimulation in our model.