Distributions of the Longest Excursions in a Tied Down Simple Random Walk and in a Brownian Bridge release_ulthi5mnufcm7e3pu4kapxiihi

by Andreas Lindell, Lars Holst

Published in Journal of Applied Probability by Cambridge University Press (CUP).

Volume 44, Issue 04 p1056-1067 (2007)


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.
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Year   2007
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