A NONCLASSICAL LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED PARTIAL SUMS

Title
A NONCLASSICAL LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED PARTIAL SUMS
Author(s)
황교신Pang, T. -X.[Pang, T. -X.]
Keywords
RANDOM-VARIABLES; LARGE DEVIATIONS; THEOREM
Issue Date
201311
Publisher
SPRINGER
Citation
ACTA MATHEMATICA HUNGARICA, v.141, no.3, pp.238 - 253
Abstract
Let {X-n, n >= 1} be a sequence of nondegenerate, symmetric, i.i.d. random variables which are in the domain of attraction of the normal law with zero means and possibly infinite variances. Denote S-n = Sigma(n)(i=1) X-i, V-n(2) = Sigma(n)(i=1) X-i(2). Then we prove that there is a sequence of positive constants {(b) over bar (n), n >= 1} which is defined by Klesov and Rosalsky [11], is monotonically approaching infinity and is not asymptotically equivalent to log log n but is such that limsup(n -> 8) vertical bar S-n vertical bar/root 2V(n)(2)b(n) = 1 almost surely if some additional technical assumptions are imposed.
URI
http://hdl.handle.net/YU.REPOSITORY/28509http://dx.doi.org/10.1007/s10474-013-0323-y
ISSN
0236-5294
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기초교육대학 > 교양학부 > Articles
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