Asymptotic behavior of densities of unimodal convolution semigroups

Wojciech Cygan; Tomasz Grzywny; Bartosz Trojan

doi:10.1090/tran/6830

Asymptotic behavior of densities of unimodal convolution semigroups

Probability 2018-11-29 v2 Functional Analysis

Authors: Wojciech Cygan , Tomasz Grzywny , Bartosz Trojan

View on arXiv ↗ PDF ↗ DOI ↗

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 L\'{e}vy--Khintchine exponent is regularly varying of index between $0$ and $2$ .

Keywords

unimodal convolution semigroup transition density asymptotic formula Lévy-Khintchine exponent regular variation probability measure isotropic

Cite

@article{arxiv.1504.08358,
  title  = {Asymptotic behavior of densities of unimodal convolution semigroups},
  author = {Wojciech Cygan and Tomasz Grzywny and Bartosz Trojan},
  journal= {arXiv preprint arXiv:1504.08358},
  year   = {2018}
}

Comments

We added Section 3; paper accepted in Transactions of AMS

Related papers

View all related →