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Limit theorems for random transformations and processes in random environments


Author: Yuri Kifer
Journal: Trans. Amer. Math. Soc. 350 (1998), 1481-1518
MSC (1991): Primary 60F05; Secondary 58F15, 60J99, 60J05
DOI: https://doi.org/10.1090/S0002-9947-98-02068-6
MathSciNet review: 1451607
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Abstract: I derive general relativized central limit theorems and laws of iterated logarithm for random transformations both via certain mixing assumptions and via the martingale differences approach. The results are applied to Markov chains in random environments, random subshifts of finite type, and random expanding in average transformations where I show that the conditions of the general theorems are satisfied and so the corresponding (fiberwise) central limit theorems and laws of iterated logarithm hold true in these cases. I consider also a continuous time version of such limit theorems for random suspensions which are continuous time random dynamical systems.


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Additional Information

Yuri Kifer
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
Email: kifer@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9947-98-02068-6
Keywords: Central limit theorem, random transformations, random environment
Received by editor(s): July 16, 1996
Additional Notes: Supported by the US-Israel Binational Science Foundation
Article copyright: © Copyright 1998 American Mathematical Society

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