Abstract
We construct bicategories of Markov processes where the objects are input and output sets, the morphisms (one-cells) are Markov processes and the two-cells are simulations. This builds on the work of Baez, Fong and Pollard, who showed that a certain kind of finite-space continuous-time Markov chain (CTMC) can be viewed as morphisms in a category. This view allows a compositional description of their CTMCs. Our contribution is to develop a notion of simulation between processes and construct a bicategory where the two-cells are simulation morphisms. Our version is for processes that are essentially probabilistic transition systems with discrete time steps and which do not satisfy a detailed balance condition. We have also extended the theory to continuous space processes.
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Acknowledgements
We are very grateful to Brendan Fong for helpful discussions. We thank the reviewers for their detailed comments and feedback. This research has been supported by a research grant from NSERC.
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Clerc, F., Humphrey, H., Panangaden, P. (2017). Bicategories of Markov Processes. In: Aceto, L., Bacci, G., Bacci, G., Ingólfsdóttir, A., Legay, A., Mardare, R. (eds) Models, Algorithms, Logics and Tools. Lecture Notes in Computer Science(), vol 10460. Springer, Cham. https://doi.org/10.1007/978-3-319-63121-9_6
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DOI: https://doi.org/10.1007/978-3-319-63121-9_6
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