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J. Korean Math. Soc. 1996; 33(4): 983-992
Printed December 1, 1996
Copyright © The Korean Mathematical Society.
Limit theorems for markov processes generated by iterations of random maps
Oesook Lee
Ewha Womans University
We consider the asymptotic behaviors of Markov process which is generated by successive iterations of independent and identically distributed random maps. We show that average contraction of some finite compositions of random maps is sufficient for the existence of a unique invariant measure. A functional central limit theorem and a strong law of large numbers are proved for arbitrary Lipschitzian functions.
Keywords: Markov process, invariant probability, weak convergence, strong law of large numbers, functional central limit theorem
MSC numbers: 60J05, 60F05
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