Asymptotical properties of distributions of isotropic Levy processes

作者：Kim Panki^*; Mimica Ante

来源：Stochastic Processes and Their Applications, 2018, 128(8): 2688-2709.

DOI：10.1016/j.spa.2017.09.017

• Asymptotic
• Transition density
• Levy process
• Unimodal Levy process
• Heat kernel
• Laplace exponent
• Levy measure
• Subordinator
• Subordinate Brownian motion

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))).

• 出版日期2018-8