Excursions Away from a Regular Point for One-Dimensional Symmetric Lévy Processes without Gaussian Part

The characteristic measure of excursions away from a regular point is studied for a class of symmetric Lévy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result is applied to prove extremeness of the excursion measure and...

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Bibliographic Details
Published inPotential analysis Vol. 32; no. 4; pp. 305 - 341
Main Author Yano, Kouji
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.05.2010
Subjects
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
60J50
Lévy process
60G51
Extreme points
Excursion theory
Feller property
60G17
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Summary:The characteristic measure of excursions away from a regular point is studied for a class of symmetric Lévy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result is applied to prove extremeness of the excursion measure and to prove several sample path behaviors of the excursion and the h -path processes.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-009-9152-6