Abstract
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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–Khinchin 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–Khinchin 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.
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Keywords
quasi-infinitely divisible laws, characteristic functions,
the Lévy–Khinchin formula, weak convergence
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Mathematical Subject Classification
Primary: 60E05, 60E07, 60E10, 60F05
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Milestones
Received: 15 June 2022
Accepted: 5 February 2023
Published: 23 May 2023
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