CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
|
1991年
/
43卷
/
05期
关键词:
D O I:
10.4153/CJM-1991-052-0
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
It is a well known fact that for rapidly increasing n(k) the sequence (cos n(k)x)k = 1 infinity behaves like a sequence of independent random variables; in particular N-1/2-SIGMA-k less-than-or-equal-to N cos n(k)x has a limiting Gaussian distribution as N --> infinity. Under a certain critical speed (actually n(k) approximately e square-root k) this result breaks down and (cos n(k)x)k = 1 infinity becomes strongly dependent. The purpose of this paper is to investigate the asymptotic behavior of normed sums a(N)-1-SIGMA-k less-than-or-equal-to N cos n(k)x in the strongly dependent domain; specifically, we construct a large class of nongaussian limit distributions of such sums.