On the almost sure central limit theorem for self-normalized products of partial sums of phi-mixing random variables

Title
On the almost sure central limit theorem for self-normalized products of partial sums of phi-mixing random variables
Author(s)
황교신
Keywords
SEQUENCES; ASSOCIATION
Issue Date
201304
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
Citation
JOURNAL OF INEQUALITIES AND APPLICATIONS
Abstract
Let {X-n, n >= 1} be a sequence of strictly stationary phi-mixing positive random variables which are in the domain of attraction of the normal law with EX1 = mu > 0, possibly infinite variance and mixing coefficient rates phi(n) satisfying Sigma(n >= 1)phi(1/2)(2(n))< infinity . Under suitable conditions, we here give an almost sure central limit theorem for self-normalized products of partial sums, i.e., lim (n ->infinity) 1/D-n Sigma(n)(m-1) d(m)l ((Pi(m)(k=1) S-k/k mu)mu/((beta Vm)) <= X) = F( x) a.s. foranyx is an element of R, where F is the distribution function of the random variable e(root 2N) and N is a standard normal random variable.
URI
http://hdl.handle.net/YU.REPOSITORY/26050http://dx.doi.org/10.1186/1029-242X-2013-155
ISSN
1029-242X
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기초교육대학 > 교양학부 > Articles
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