Bicategories of Markov Processes

  • Florence Clerc
  • Harrison Humphrey
  • Prakash PanangadenEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10460)


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.



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Florence Clerc
    • 1
  • Harrison Humphrey
    • 1
  • Prakash Panangaden
    • 1
    Email author
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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