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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1999; 36(4): 737-746

Printed July 1, 1999

Copyright © The Korean Mathematical Society.

Stationary solutions for iterated function systems controlled by stationary processes

O. Lee and D.W. Shin

Abstract

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We consider a class of discrete parameter processes on a locally compact Banach space $ S$ arising from successive compositions of strictly stationary random maps with state space $C(S,S)$, where $C(S,S)$ is the collection of continuous functions on $S$ into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

Keywords: stationary process, iteration of random maps, Lipschitz maps, convergence in distribution

MSC numbers: 60J05, 60F05

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