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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Markov chains in random environments and random iterated function systems


Author: Örjan Stenflo
Journal: Trans. Amer. Math. Soc. 353 (2001), 3547-3562
MSC (2000): Primary 28A80, 37H99, 60F05, 60J05, 60K37; Secondary 28A78, 60G57, 65C05
Published electronically: April 18, 2001
MathSciNet review: 1837247
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Abstract:

We consider random iterated function systems giving rise to Markov chains in random (stationary) environments. Conditions ensuring unique ergodicity and a ``pure type'' characterization of the limiting ``randomly invariant'' probability measure are provided. We also give a dimension formula and an algorithm for simulating exact samples from the limiting probability measure.


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Additional Information

Örjan Stenflo
Affiliation: Department of Mathematics, UmeåUniversity, SE-90187 Umeå, Sweden
Email: stenflo@math.umu.se

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02798-2
PII: S 0002-9947(01)02798-2
Keywords: Iterated Function Systems (IFS), Markov chains, pointwise dimension, random environments, exact sampling
Received by editor(s): December 19, 1999
Received by editor(s) in revised form: October 2, 2000
Published electronically: April 18, 2001
Additional Notes: Supported by the The Royal Swedish Academy of Sciences
Article copyright: © Copyright 2001 American Mathematical Society