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CONTRACTIVE MARKOV SYSTEMS

Published online by Cambridge University Press:  04 February 2005

IVAN WERNER
IVAN WERNER
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, United Kingdomiw11@st-andrews.ac.uk
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Abstract

Certain discrete-time Markov processes on locally compact metric spaces which arise from graph-directed constructions of fractal sets with place-dependent probabilities are studied. Such systems naturally extend finite Markov chains and inherit some of their properties. It is shown that the Markov operator defined by such a system has a unique invariant probability measure in the irreducible case and an attractive probability measure in the aperiodic case if the vertex sets form an open partition of the state space, the restrictions of the probability functions on their vertex sets are Dini-continuous and bounded away from zero, and the system satisfies a condition of contractiveness on average.

Keywords

60J1028A8037A50
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 236 - 258
Copyright
The London Mathematical Society 2005

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