SFB 303 Discussion Paper No. A - 371

Author: Evstigneev, I. V., and P. E. Greenwood
Title: Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting
Abstract: In this paper we develop general techniques for working with discrete Markov fields. We illustrate these techniques in a variety of random field models which have physical interpretations.
We concentrate on the two related problems:
(a) At what random elements of the index set T is the Markov property retained?
(b) What random transformations of the index set preserve the Markov property of the field?
Problems (a) and (b) are fundamental in the classical theory of Markov processes (e.g. Dynkin (1965)). If the Markov property holds at a class of random indices, the property is termed a "strong Markov" property. Results identifying such classes are useful general tools for studying Markov random processes and fields.
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Creation-Date: June 1993
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