Geometrical aspects of the theory of non-homogeneous Markov chains

1 January 1975

journal article
research article
Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society

Vol. 77 (1) , 171-183
https://doi.org/10.1017/s0305004100049501

Abstract

A geometrical representation of the transition matrices of a non-homogeneous chain with N states, in terms of certain convex subsets of , is used to describe aspects of the chain. For example, an important theorem of Cohn on the structure of the tail σ-field is a simple corollary. The embedding problem is shown to be entirely geometrical in character. The representation extends to Markov processes on quite general state spaces, and the tail is then represented by the projective limit of these convex sets.

Keywords

This publication has 13 references indexed in Scilit:

On the historical development of the theory of finite inhomogeneous Markov chains
Mathematical Proceedings of the Cambridge Philosophical Society, 1973
The combinatorial structure of non-homogeneous Markov chains
Probability Theory and Related Fields, 1973
The Bang-Bang problem for stochastic matrices
Probability Theory and Related Fields, 1973
Kolmogorov's differential equations for non-stationary, countable state Markov processes with uniformly continuous transition probabilities
Mathematical Proceedings of the Cambridge Philosophical Society, 1973
On Two Recent Papers on Ergodicity in Nonhomogeneous Markov Chains
The Annals of Mathematical Statistics, 1972
A characterization of minimal Markov jump processes
Probability Theory and Related Fields, 1972
On finite tail ?-algebras
Probability Theory and Related Fields, 1972
On the Tail $Sigma$-Algebra of the Finite Inhomogeneous Markov Chains
The Annals of Mathematical Statistics, 1970
Central Limit Theorem for Nonstationary Markov Chains. II
Theory of Probability and Its Applications, 1956
Central Limit Theorem for Nonstationary Markov Chains. I
Theory of Probability and Its Applications, 1956