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Measure Concentration for Stable Laws with Index Close to 2

   
@article{ECP1129,
	author = {Philippe Marchal},
	title = {Measure Concentration for Stable Laws with Index Close to 2},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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.},
	pages = {no. 4, 29-35},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1129},    
        url = {http://ecp.ejpecp.org/article/view/1129}}