Electronic Communications in Probability

Electronic Communications in Probability > Vol. 10 (2005) > Paper 4

Measure Concentration for Stable Laws with Index Close to 2

Philippe Marchal, Université Paris 6

Abstract
We give upper bounds for the probability $P(|f(X)-Ef(X)|>x)$, where $X$ is a stable random variable with index close to 2 and $f$ is a Lipschitz function. While the optimal upper bound is known to be of order $1/x^alpha$ for large $x$, we establish, for smaller $x$, an upper bound of order $exp(-x^alpha/2)$, which relates the result to the gaussian concentration.

Full text: PDF

Pages: 29-35

Published on: February 25, 2005

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Electronic Communications in Probability. ISSN: 1083-589X