Download this article
 Download this article For screen
For printing
Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On weak convergence of quasi-infinitely divisible laws

Alexey Khartov

Vol. 322 (2023), No. 2, 341–367
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–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.

Keywords
quasi-infinitely divisible laws, characteristic functions, the Lévy–Khinchin formula, weak convergence
Mathematical Subject Classification
Primary: 60E05, 60E07, 60E10, 60F05
Milestones
Received: 15 June 2022
Accepted: 5 February 2023
Published: 23 May 2023
Authors
Alexey Khartov
Laboratory for Approximation Problems of Probability
Smolensk State University
Smolensk
Russia

Open Access made possible by participating institutions via Subscribe to Open.