Limit theorems for random transformations and processes in random environments

Kifer, Yuri

doi:10.1090/S0002-9947-98-02068-6

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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