Stationary Markov Sets.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1986
- Accession Number
- ADA170109
Entities
People
- Michael I. Taksar
Organizations
- Florida State University