Stability and attraction to normality for Lévy processes at zero and at infinity
type: Item
instance of: scholarly article
title: Stability and attraction to normality for Lévy processes at zero and at infinity
zbMATH Open document ID: 1015.60043
DOI: 10.1023/A:1016228101053
published in: Journal of Theoretical Probability
publication date: 2003-04-03T00:00:00Z
review text: For a Lévy process \(X_t\) the weak and almost sure behaviour is considered for \(X_t/b(t)\to 1\) and \(X_t/t \to\delta\) as \(t\downarrow 0\) or \(t\to \infty\). Necessary and sufficient conditions are obtained expressed in terms of characteristics directly available from the characteristic functions of the process. The convergence of these ratios to infinity and the weak convergence to normal distributions are considered as well.
reviewed by: Nijolė Kalinauskaitė
Mathematics Subject Classification ID: 60G51
zbMATH DE Number: 1892246
zbMATH Keywords: Lévy processes
zbMATH Keywords: relative stability
zbMATH Keywords: asymptotic normality
zbMATH Keywords: domains of attraction
author: Ronald A. Doney
author: Ross A. Maller
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1892246