Approximating Markov Processes by Averaging

  • Philippe Chaput
  • Vincent Danos
  • Prakash Panangaden
  • Gordon Plotkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5556)

Abstract

We take a dual view of Markov processes – advocated by Kozen – as transformers of bounded measurable functions. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results:

(i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximation. (iii) It is possible to show that there is a minimal bisimulation equivalent to a process obtained as the limit of the finite approximants.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Philippe Chaput
    • 1
  • Vincent Danos
    • 2
  • Prakash Panangaden
    • 1
  • Gordon Plotkin
    • 2
  1. 1.School of Computer ScienceMcGill University 
  2. 2.School of InformaticsUniversity of Edinburgh 

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