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Naive asymptotics for hitting time bounds in Markov chains

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Abstract

A set of sufficient conditions is obtained for Markov chains to yield upper and lower passage time bounds. While obtaining expected passage times is strictly a numerical procedure for general Markov chains, the results presented here outline a simple approach to bound expected passage times provided the chains satisfy certain easy to check criteria. The results may be useful in modelling situations, such as in the analysis of algorithms, where simple ways of obtaining average complexity estimates are required.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, 47906, West Lafayette, IN, USA

    Vernon Rego

Authors
  1. Vernon Rego
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Additional information

Research performed at the Mathematical Sciences Section of Oak Ridge National Laboratory under the auspices of the Faculty Research Participation Program of Oak Ridge Associated Universities, and supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. DOE, under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.

Also supported in part by the National Science Foundation, under award ASC-9002225 and NATO award CRG900108

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Rego, V. Naive asymptotics for hitting time bounds in Markov chains. Acta Informatica 29, 579–594 (1992). https://doi.org/10.1007/BF01185562

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  • DOI: https://doi.org/10.1007/BF01185562

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