Some Peculiar Semi-Markov Processes
Abstract
Experience with semi-Markov processes with finite expected waits suggests that the behavior of Markov processes is a good guide to understanding the behavior of the more general process. However, examples are given to show that when expected waits are infinite quite surprising behavior is possible. For a two-state aperiodic semi-Markov process the instantaneous state probabilities Pi(t) can have (C, l)-limits but not strict limits; for a three-state (and irreducible) process one can have Po(t) tend to a strict limit as t - infinity but Pi(t) and P2(t)not even have (C, l)-limits. For an aperiodic irreducible infinite chain one can have Pi(t) - pi i > 0 as t - infinity, for every i, yet Epsilon pi i < 1.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD1027217
Entities
People
- Walter L. Smith
Organizations
- University of North Carolina at Chapel Hill