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A Note on Error Bounds for Approximating Transition Probabilities in Continuous-time Markov Chains

Published online by Cambridge University Press:  27 July 2009

Nico M. van Dijk
Nico M. van Dijk
Affiliation:
Department of EconometricsFree University, Amsterdam, The Netherlands
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Abstract

Recently, Ross [1] proposed an elegant method of approximating transition probabilities and mean occupation times in continuous-time Markov chains based upon recursively inspecting the process at exponential times. The method turned out to be amazingly efficient for the examples investigated. However, no formal rough error bound was provided. Any error bound even though robust is of practical interest in engineering (e.g., for determining truncation criteria or setting up an experiment). This note primarily aims to show that by a simple and standard comparison relation a rough error bound of the method is secured. Also, some alternative approximations are inspected.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 4 , October 1988 , pp. 471 - 474
Copyright
Copyright © Cambridge University Press 1988

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References

1.Ross, S.M. (1987). Approximating transition probabilities and mean occupation times in continuous-time Markov chains. Probability in the Engineering and Informational Sciences I: 251–264.Google Scholar
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