Electronic Resource
Springer
Journal of theoretical probability
9 (1996), S. 1039-1056
ISSN:
1572-9230
Keywords:
Scaled sample
;
random series
;
concentration of measure
;
probability inequalities
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The scaled-sample property ({X j /γ n } j=1 n →K a.s. asn→∞, whereγ n 〈0 andX( j ) are i.i.d. with law μ) is investigated for distributions μ which are the laws of random series of form ∑ i=1 ∞ X i v i . Herev i are fixed vectors in a Banach space, andX i are i.i.d. real-valued with common lawμ 1. The main result presented here establishes this convergence for a large collection of possible distributionsμ 1, including some discrete examples. The main tools used are probability inequalities on the tails of the series, and concentration of measure arguments.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02214264
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