On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum
type: Item
instance of: scholarly article
title: On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum
zbMATH Open document ID: 1049.60042
DOI: 10.1023/B:JOTP.0000020481.14371.37
published in: Journal of Theoretical Probability
publication date: 2004-08-06T00:00:00Z
review text: Let \(X\) be a spectrally one-sided Lévy process and reflect it at its past infimum \(I\). That is the Lévy process minus its past infimum \(Y=X-I\). The author studies such a process. Here he determines the Laplace transform for \(Y\) if \(X\) is spectrally negative. Subsequently, he finds an expression for the resolvent measure for \(Y\) killed upon leaving \([0,a]\) and studies some properties of this process. Finally, the rate of convergence of the supremum of the reflected process to \(a\) is given.
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 2083466
zbMATH Keywords: reflected Lévy process
zbMATH Keywords: resolvent measure
zbMATH Keywords: Laplace transform
author: Martijn R. Pistorius
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: b:jotp.0000020481.14371.37
OpenAlex ID: W1973018627
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description: scientific article; zbMATH DE number 2083466