ON FINITE RANGE STABLE-TYPE CONCENTRATION

摘要

We first study the deviation probability where is a Lipschitz (for the Euclidean norm) function defined on Rd and X is an a-stable random vector ofindex a 6 (1,2) We show that this probability is upper bounded by either according to x taking small values or being in a finite range interval. We generalize these finite range concentration inequalities to where F is a stochastic functional on the Poisson space equipped with a stable Levy measure of index a e (0, 2) and where m{F) is a median of F.