Limit theorems for random transformations and processes in random environments

Yuri Kifer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

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.

Original languageEnglish
Pages (from-to)1481-1518
Number of pages38
JournalTransactions of the American Mathematical Society
Volume350
Issue number4
DOIs
StatePublished - 1998

Keywords

  • Central limit theorem
  • Random environment
  • Random transformations

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