Concentration of measures via size-biased couplings
成果类型：
Article
署名作者：
Ghosh, Subhankar; Goldstein, Larry
署名单位：
University of Southern California
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-009-0253-3
发表日期：
2011
页码：
271-278
关键词：
摘要：
Let Y be a nonnegative random variable with mean mu and finite positive variance sigma(2), and let Y-s, defined on the same space as Y, have the Y size-biased distribution, characterized by E[Yf(Y)] = mu Ef(Y-s) for all functions f for which these expectations exist. Under a variety of conditions on Y and the coupling of Y and Ys, including combinations of boundedness and monotonicity, one sided concentration of measure inequalities such as p (Y - mu / sigma >= t) <= exp (-t(2) / 2(A + Bt) for all t > 0 hold for some explicit A and B. The theorem is applied to the number of bulbs switched on at the terminal time in the so called lightbulb process ofRao et al. (Sankhy (a) over bar 69: 137-161, 2007).
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