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.
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