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Symmetric Stable Laws and Stable-Like Jump-Diffusions
Authors:Kolokoltsov  Vassili
Institution:Department of Mathematics, Statistics and Operational Research, Nottingham Trent University Burton Street, Nottingham, NG1 4BU, vk{at}maths.ntu.ac.uk
Abstract:Asymptotic expansions are obtained for finite-dimensional symmetricstable distributions. They are used to prove the existence ofcontinuous transition probability densities of stable and stable-likejump-diffusions, and to construct local multiplicative asymptoticsandglobal two-sided estimates for these densities. As a consequence,the distribution of the first passage times for stable jump-diffusionsis estimated and the integral test for the limsup behaviourof their sample paths as t -> 0 is provided. 1991 MathematicsSubject Classification: 60E07, 60G17, 60J35, 47D07.
Keywords:stable laws  asymptotic expansions  transition probability density  stable jump-diffusion  two-sided estimates
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