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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Limit theorems for random transformations and processes in random environments
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by Yuri Kifer PDF
Trans. Amer. Math. Soc. 350 (1998), 1481-1518 Request permission

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
  • Received by editor(s): July 16, 1996
  • Additional Notes: Supported by the US-Israel Binational Science Foundation
  • © Copyright 1998 American Mathematical Society
  • 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