Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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.