The Most Visited Sites of Certain Lévy Processes

Michael B. Marcus ()
Additional contact information
Michael B. Marcus: CUNY

Journal of Theoretical Probability, 2001, vol. 14, issue 3, 867-885

Abstract: Abstract Let X be a symmetric Lévy process with $$Ee^{i\lambda X_t } = e^{ - t\psi (\lambda )}$$ Let $$\phi (x) = \frac{2}{\pi }\int_0^\infty {\frac{{1 - \cos \lambda x}}{{\psi (\lambda )}}} d\lambda $$ Assume that • ψ(λ) is regularly varying at zero with index 1 9 $$\mathop {\lim }\limits_{t \to \infty } \frac{{\left| {V(t)} \right|}}{{\phi ^{ - 1} \left( {\frac{{t\psi ^{ - 1} (1/t)}}{{(\log t)^\gamma }}} \right)}} = \infty {\text{ a}}{\text{.s}}{\text{.}}$$ This result is obtained for symmetric stable processes in the above reference. We use their approach and many of their methods.

Keywords: local times; Lévy processes; most visited sites; Gaussian processes with stationary increments (search for similar items in EconPapers)
Date: 2001
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1012295810270 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:14:y:2001:i:3:d:10.1023_a:1012295810270

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1012295810270

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().