Transition densities of subordinators of positive order

Tomasz Grzywny; Łukasz Leżaj; Bartosz Trojan

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arXiv · 1812.06793

Transition densities of subordinators of positive order

Tomasz Grzywny·Łukasz Leżaj·Bartosz Trojan

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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.

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Tomasz Grzywny, Łukasz Leżaj, Bartosz Trojan. 2018-12-17. Transition densities of subordinators of positive order. https://arxiv.org/abs/1812.06793

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