UZH-Logo

Maintenance Infos

Functional limit theorems for Lévy processes satisfying Cramér's condition


Bertoin, J; Barczy, M (2011). Functional limit theorems for Lévy processes satisfying Cramér's condition. Electronic Journal of Probability, 16:2020 -2038.

Abstract

We consider a Lévy process that starts from x<0 and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as x goes to −∞ for the law of the (two-sided) path shifted at the first instant when it enters (0,∞), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.

We consider a Lévy process that starts from x<0 and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as x goes to −∞ for the law of the (two-sided) path shifted at the first instant when it enters (0,∞), respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.

Citations

3 citations in Web of Science®
3 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

44 downloads since deposited on 24 Apr 2013
39 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:24 Apr 2013 14:34
Last Modified:05 Apr 2016 16:43
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v16-930
Permanent URL: https://doi.org/10.5167/uzh-77141

Download

[img]
Preview
Filetype: PDF
Size: 210kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations