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Distributions of the longest excursions in a tied down simple random walk and in a Brownian bridge
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2007 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 44, no 4, 1056-1067 p.Article in journal (Refereed) Published
Abstract [en]

Expressions for the joint distribution of the longest and second longest excursions as well as the marginal distributions of the three longest excursions in the Brownian bridge are obtained. The method, which primarily makes use of the weak convergence of the random walk to the Brownian motion, principally gives the possibility to obtain any desired joint or marginal distribution. Numerical illustrations of the results are also given.

Place, publisher, year, edition, pages
2007. Vol. 44, no 4, 1056-1067 p.
Keyword [en]
tied down random walk, Brownian bridge, ranked excursion length, weak, convergence, generating function, Kummer function
URN: urn:nbn:se:kth:diva-17207DOI: 10.1239/jap/1197908824ISI: 000252596500017ScopusID: 2-s2.0-38949160744OAI: diva2:335250
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Holst, Lars
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