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August 2002 Almost sure convergence for iterated functions of independent random variables
Jonathan Jordan
Ann. Appl. Probab. 12(3): 985-1000 (August 2002). DOI: 10.1214/aoap/1031863178


We consider a class of probabilistic models obtained by iterating random functions of $k$ random variables. We prove an analogue of the weak law of large numbers and under a symmetry condition we prove a strong law. The symmetry condition is satisfied if the initial random variables are exchangeable. Our results can be used to give stronger results than those previously obtained in the special case where the function is deterministic. Both types of models have applications in physics and in computer science.


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Jonathan Jordan. "Almost sure convergence for iterated functions of independent random variables." Ann. Appl. Probab. 12 (3) 985 - 1000, August 2002.


Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1012.60034
MathSciNet: MR1925449
Digital Object Identifier: 10.1214/aoap/1031863178

Primary: 60F15
Secondary: 60F05 , 60K35 , 60K37

Keywords: asymptotic behavior , Hierarchical systems , laws of large numbers

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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