Critical LIL behavior of the trigonometric system
Author:
I. Berkes
Journal:
Trans. Amer. Math. Soc. 338 (1993), 553585
MSC:
Primary 60F15; Secondary 42A55
MathSciNet review:
1099352
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Abstract: It is a classical fact that for rapidly increasing the sequence behaves like a sequence of i.i.d. random variables. Actually, this almost i.i.d. behavior holds if grows faster than ; below this speed we have strong dependence. While there is a large literature dealing with the almost i.i.d. case, practically nothing is known on what happens at the critical speed (critical behavior) and what is the probabilistic nature of in the strongly dependent domain. In our paper we study the critical LIL behavior of i.e., we investigate how classical fluctuational theorems like the law of the iterated logarithm and the KolmogorovFeller test turn to nonclassical laws in the immediate neighborhood of .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199310993522
PII:
S 00029947(1993)10993522
Keywords:
Lacunary trigonometric series,
weak and strong dependence,
law of the iterated logarithm,
upperlower class tests
Article copyright:
© Copyright 1993
American Mathematical Society
