On weak convergence of quasi-infinitely divisible laws

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 Lévy--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 Lévy--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.

References in corpus (1)

• A complete Riemann zeta distribution and the Riemann hypothesis

Cited by in corpus (1)

• The class $\mathbf{Q}$ and mixture distributions with dominated continuous singular parts