Asymptotic behaviour and estimates of slowly varying convolution semigroups

Abstract

We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on ${\mathbb{R}}^d$ under the assumption that its Lévy--Khintchine exponent varies slowly. We also derive some new estimates of the transition densities and Green functions.

35 pages

References in corpus (4)

• On Harnack inequality and Hölder regularity for isotropic unimodal Lévy processes
• Estimates of transition densities and their derivatives for jump Lévy processes
• Asymptotic behavior of densities of unimodal convolution semigroups
• On the small-time behaviour of Lévy-type processes

Cited by in corpus (7)

• Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes
• Asymptotic behavior of densities of unimodal convolution semigroups
• Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces
• Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps
• Subordinated Markov processes: sharp estimates for heat kernels and Green functions
• An $L_q(L_p)$-theory for time-fractional diffusion equations with nonlocal operators generated by Lévy processes with low intensity of small jumps
• Heat kernel estimates for anisotropic symmetric jump processes