On weak convergence of quasi-infinitely divisible laws
Probability
2023-05-24 v1
Abstract
We study a new class of so-called quasi-infinitely divisible laws, which is a wide natural extension of the well known class of infinitely divisible laws through the L\'evy--Khinchine type representations. We are interested in criteria of weak convergence within this class. Under rather natural assumptions, we state assertions, which connect a weak convergence of quasi-infinitely divisible distribution functions with one special type of convergence of their L\'evy--Khinchine spectral functions. The latter convergence is not equivalent to the weak convergence. So we complement known results by Lindner, Pan, and Sato (2018) in this field.
Keywords
Cite
@article{arxiv.2204.13667,
title = {On weak convergence of quasi-infinitely divisible laws},
author = {A. A. Khartov},
journal= {arXiv preprint arXiv:2204.13667},
year = {2023}
}