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Linear functionals and Markov chains associated with Dirichlet processes

Published online by Cambridge University Press:  04 October 2011

Paul D. Feigin  and
Richard L. Tweedie
Paul D. Feigin
Affiliation:
Technion, Haifa and Division of Mathematics and Statistics, CSIRO
Richard L. Tweedie
Affiliation:
Siromath Pty. Ltd., Sydney and Bond University, Gold Coast, Australia
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Abstract

By investigating a Markov chain whose limiting distribution corresponds to that of the Dirichlet process we are able directly to ascertain conditions for the existence of linear functionals of that process. Together with earlier analyses we are able to characterize those functionals which are a.s. finite in terms of the parameter measure of the process. We also show that the appropriate Markov chain in the space of measures is only weakly convergent and not Harris ergodic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 579 - 585
Copyright
Copyright © Cambridge Philosophical Society 1989

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