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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
DOI: 10.2307/1427457
Stable URL: http://www.jstor.org/stable/1427457
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Representation of Symmetric Transition Functions
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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.

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