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On the representation of symmetric transition functions

Published online by Cambridge University Press:  01 July 2016

W. J. Anderson  and
P. M. McDunnough
W. J. Anderson*
Affiliation:
McGill University
P. M. McDunnough*
Affiliation:
University of Toronto
*
∗Postal address: Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke St West, Montreal, Canada H3A 2K6.
∗∗Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 1A1.
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Abstract

In this paper, we give an alternative derivation of Kendall's representation for symmetric transition functions which relies on the backward and/or forward integral recursions. The proof uses a lemma concerning approximation by finite sections (which is useful in its own right) and is similar to the original proof for birth and death processes by Lederman and Reuter. Finally, we obtain a general result guaranteeing the existence of representations of transition functions such as those obtained by Pruitt and Iglehart.

Keywords

CONTINUOUS-TIME MARKOV CHAINSREVERSIBLEORTHOGONALq-MATRIX
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 548 - 563
Copyright
Copyright © Applied Probability Trust 1990 

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