Density and tails of unimodal convolution semigroups
Krzysztof Bogdan, Tomasz Grzywny, Micha{\l} Ryznar
TL;DR
This paper provides precise bounds for isotropic unimodal convolution semigroups with Le9vy-Khintchine exponents having Matuszewska indices between 0 and 2, enhancing understanding of their density and tail behaviors.
Contribution
It introduces sharp bounds for these semigroups based on the properties of their Le9vy-Khintchine exponents, a novel approach in this context.
Findings
Established bounds for densities of the semigroups.
Characterized tail behaviors based on Matuszewska indices.
Extended understanding of unimodal convolution semigroups.
Abstract
We give sharp bounds for the isotropic unimodal probability convolution semigroups when their L\'evy-Khintchine exponent has Matuszewska indices strictly between 0 and 2.
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