#
Approximating Continuous Markov Processes

Josee Desharnais, Vineet Gupta, Radha Jagadeesan, Prakash Panangaden
### Abstract

We study approximate reasoning about continuous-state labeled
Markov processes. We show how to approximate a labeled Markov
process by a family of *finite-state* labeled Markov chains.
We show that the collection of labeled Markov processes carries a
Polish space structure with a countable basis given by finite
state Markov chains with rational probabilities. The primary
technical tools that we develop to reach these results are
- A finite-model theorem for the modal logic
used to characterize bisimulation
- A categorical equivalence between the category of Markov processes (with
simulation morphisms) with the omega-continuous dcpo
**Proc**,
defined as the solution of the recursive domain equation **Proc** =
∏_(Labels) P_(Prob)(**Proc**), where P_(Prob)(D) is
the probabilistic powerdomain of Jones and Plotkin.

The correspondence between labeled Markov processes and **Proc**
yields a logic complete for reasoning about simulation for
continuous-state processes.
© IEEE, 2000.

@InProceedings{approx-lics2000,
title = "Approximating Continuous Markov Processes",
author = "Josee Desharnais and Vineet Gupta and Radha
Jagadeesan and Prakash Panangaden"
booktitle = "Proceedings, Fifteenth Annual {IEEE} Symposium on Logic in
Computer Science",
year = "2000",
pages = "95-106",
address = "Santa Barbara, USA",
organization = "IEEE Computer Society Press"
}

Postscript file of extended abstract (220K)