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A central limit property under a modified Ehrenfest urn design

Part of: Special processes Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Yung-Pin Chen
Yung-Pin Chen*
Affiliation:
Lewis & Clark College
*
∗Postal address: Department of Mathematical Sciences, Lewis & Clark College, Portland, OR 97219, USA. Email address: ychen@lclark.edu
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Abstract

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We consider a stochastic process in a modified Ehrenfest urn model. The modification prescribes there to be a minimum number of balls in each urn, and the process records the differences between treatment assignments under a sampling scheme implemented with this modified Ehrenfest urn model. In contrast to the result that the difference process forms a Markov chain and converges to a stationary distribution under the Ehrenfest urn model, the corresponding process under this modified Ehrenfest urn design satisfies the central limit property. We prove this asymptotic normality property using a central limit theorem for dependent random variables, renewal theory, and two Kolmogorov-type maximal inequalities.

Keywords

Ehrenfest urn modelMarkov chainrenewal theorycentral limit propertymaximal inequality

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K05: Renewal theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 409 - 420
Copyright
© Applied Probability Trust 2006 

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