Stationary Markov Sets.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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A Markov set is a random set on a real line whose future shape is conditionally independent of the past shape given present. Such sets appear in the study of visiting times of special Markov but not strong Markov processes. If the Markov process is stationary then the corresponding set is also stationary, that is, its distribution does not depend on the choice of the origin on the real line. In this paper we will describe all closed stationary Markov sets. We will show that each stationary Markov which is not regenerative can be constructed from two special regenerative sets by either taing a mixture of these regenerative sets or taking a Superposition of two regenerative sets. Superposition can be described loosely as cuttingtwo real lines R1 and R2 with two sets M1 and M2 in them, into pieces of iid length and then combine them into one line alternating pieces from R1 and R2. The union of the cut offs from M1 and M2 will be the superposition of the sets M1 and M2.
- Statistics and Probability