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2005 Measure Concentration for Stable Laws with Index Close to 2
Philippe Marchal
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Electron. Commun. Probab. 10: 29-35 (2005). DOI: 10.1214/ECP.v10-1129

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.

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Philippe Marchal. "Measure Concentration for Stable Laws with Index Close to 2." Electron. Commun. Probab. 10 29 - 35, 2005. https://doi.org/10.1214/ECP.v10-1129

Information

Accepted: 25 February 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1060.60011
MathSciNet: MR2119151
Digital Object Identifier: 10.1214/ECP.v10-1129

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