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Compound Poisson approximations for word patterns under Markovian hypotheses

Part of:Limit theoremsMarkov processesCombinatorial probability

Published online by Cambridge University Press:  14 July 2016

Mark X. Geske,
Anant P. Godbole,
Andrew A. Schaffner,
Allison M. Skolnick and
Garrick L. Wallstrom
Mark X. Geske*
Affiliation:
St. Norbert College
Anant P. Godbole*
Affiliation:
Michigan Technological University
Andrew A. Schaffner*
Affiliation:
University of Washington
Allison M. Skolnick*
Affiliation:
Lehigh University
Garrick L. Wallstrom*
Affiliation:
University of Minnesota
*
∗ Postal address: CUNA Mutual Insurance Group, Madison, WI 53701, USA.
∗∗ Postal address: Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA.
∗∗∗ Postal address: Department of Statistics, University of Washington, Seattle, WA 98195, USA.
∗∗∗∗ Postal address: 88 Stratford Road, East Brunswick, NJ 08816, USA.
∗∗∗∗∗ Postal address: School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

Consider a stationary Markov chain with state space consisting of the ξ -letter alphabet set Λ= {a 1 , a 2, ···, aξ }. We study the variables M=M(n, k) and N=N(n, k), defined, respectively, as the number of overlapping and non-overlapping occurrences of a fixed periodic k-letter word, and use the Stein–Chen method to obtain compound Poisson approximations for their distribution.

Keywords

OVERLAPPING AND NON-OVERLAPPING OCCURRENCES OF WORD PATTERNSPOISSON AND COMPOUND POISSON APPROXIMATIONSTEIN–CHEN TECHNIQUECOUPLINGRATES OF CONVERGENCE TO STATIONARITY

MSC classification

Primary:60F05: Central limit and other weak theorems
Secondary:60C05: Combinatorial probability60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995, pp. 877 - 892
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This research was supported by U.S. National Science Foundation REU Grants DMS-9100829 and DMS-9200409.

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