Regular variation and free regular infinitely divisible laws

Authors

Arijit Chakrabarty, Indian Statistical Institute, Kolkata
Sukrit Chakraborty, Indian Statistical Institute, Kolkata
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Statistics and Probability Letters

Abstract

In this article the relation between the tail behaviours of a free regular infinitely divisible probability measure and its Lévy measure is studied. An important example of such a measure is the compound free Poisson distribution, which often occurs as a limiting spectral distribution of certain sequences of random matrices. We also describe a connection between an analogous classical result of Embrechts et al. (1979) and our result using the Bercovici–Pata bijection.

DOI

10.1016/j.spl.2019.108607

Publication Date

1-1-2020

Comments

Open Access, Green

Recommended Citation

Chakrabarty, Arijit; Chakraborty, Sukrit; and Hazra, Rajat Subhra, "Regular variation and free regular infinitely divisible laws" (2020). Journal Articles. 547.
https://digitalcommons.isical.ac.in/journal-articles/547