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On the Representation of Symmetric Transition Functions
W. J. Anderson and P. M. McDunnough
Advances in Applied Probability
Vol. 22, No. 3 (Sep., 1990), pp. 548-563
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1427457
Page Count: 16
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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.
Advances in Applied Probability © 1990 Applied Probability Trust