On sojourn times, excursions and spectral measures connected with quasidiffusions
type: Item
instance of: scholarly article
title: On sojourn times, excursions and spectral measures connected with quasidiffusions
zbMATH Open document ID: 0625.60093
author: Uwe Küchler
published in: Journal of Mathematics of Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: Let X be a quasidiffusion on the real line with infinitesimal operator \(D_ mD^+_ x\). The author considers excursions of X over some level b and sojourn times in an interval [0,b'] during such an excursion. The Laplace transforms are given in terms of eigenfunctions \(f_{\lambda}\) of \(D_ mD^+_ x-\lambda id.\) Let \(P_ t(b,b')\) be the time which X spends over b' during an excursion of X from zero to b occurring before the local time of X at zero equals t. This process turns out to be a compounded Poisson process. The Poisson measure with respect to the length and the maximum of an excursion is again given in dependence of eigenfunctions.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 4015873
zbMATH Keywords: quasidiffusion
zbMATH Keywords: Laplace transforms
zbMATH Keywords: local time
zbMATH Keywords: compounded Poisson process
zbMATH Keywords: Poisson measure
zbMATH Keywords: eigenfunctions
reviewed by: Uwe Rösler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520875
OpenAlex ID: W1582041935
DOI: 10.1215/KJM/1250520875
description: scientific article; zbMATH DE number 4015873