The Arcsine Law

J. Hoffmann-Jørgensen ()
Additional contact information
J. Hoffmann-Jørgensen: University of Aarhus

Journal of Theoretical Probability, 1999, vol. 12, issue 1, 131-145

Abstract: Abstract Let N n denote the number of positive sums in the first n trials in a random walk (S i) and let L n denote the first time we obtain the maximum in S 0,..., S n. Then the classical equivalence principle states that N n and L n have the same distribution and the classical arcsine law gives necessary and sufficient condition for (1/n) L n or (1/n) N n to converge in law to the arcsine distribution. The objective of this note is to provide a simple and elementary proof of the arcsine law for a general class of integer valued random variables (T n) and to provide a simple an elementary proof of the equivalence principle for a general class of integer valued random vectors (N n, L n).

Keywords: Random walk; arcsine law (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1021748727681 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:12:y:1999:i:1:d:10.1023_a:1021748727681

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

DOI: 10.1023/A:1021748727681

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 ().