TY - JOUR
T1 - Limit theorems for random transformations and processes in random environments
AU - Kifer, Yuri
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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.
KW - Central limit theorem
KW - Random environment
KW - Random transformations
UR - http://www.scopus.com/inward/record.url?scp=22044456407&partnerID=8YFLogxK
U2 - 10.1090/s0002-9947-98-02068-6
DO - 10.1090/s0002-9947-98-02068-6
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AN - SCOPUS:22044456407
SN - 0002-9947
VL - 350
SP - 1481
EP - 1518
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 4
ER -