Asymptotical properties of distributions of isotropic Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Kim, Panki¹ 

[1] Seoul Natl Univ, Dept Math Sci, Bldg 27,1 Gwanak Ro, Seoul 08826, South Korea

关键词: Asymptotic;    Transition density;    Levy process;    Unimodal Levy process;    Heat kernel;    Laplace exponent;    Levy measure;    Subordinator;    Subordinate Brownian motion;   

DOI  :  10.1016/j.spa.2017.09.017

来源: Elsevier

【 摘 要 】

In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic Levy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise asymptotic behaviors of the tail probability of subordinators when the scaling order is between 0 and 1 including 1. The asymptotic expressions are given in terms of the radial part of characteristic exponent psi and its derivative. In particular, when psi(lambda) - lambda/2 psi'(lambda) varies regularly, as t psi(r(-1))(2)/psi(r(-1)) -(2r)(-1)psi'(r(-1)) -> 0 the tail i probability (vertical bar X-t vertical bar >= r) is asymptotically equal to a constant times t(psi(r(-1)) - (2r)(-1)psi'(r(-1))). (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free