English

Transition densities of subordinators of positive order

Probability 2020-11-24 v2 Analysis of PDEs

Abstract

We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density. Sharp estimates are provided if additional upper scaling condition on the Laplace exponent is imposed. In particular, we cover the case when the (minus) second derivative of the Laplace exponent is a function regularly varying at infinity with regularity index bigger than -2.

Keywords

Cite

@article{arxiv.1812.06793,
  title  = {Transition densities of subordinators of positive order},
  author = {Tomasz Grzywny and Łukasz Leżaj and Bartosz Trojan},
  journal= {arXiv preprint arXiv:1812.06793},
  year   = {2020}
}

Comments

Important changes in Section 4. Change of title from "Transition densities of subordinators" to "Transition densitites of subordinators of positive order"