Functionals of Brownian Meander and Brownian Excursion

Brownian Motion, Bridge, Excursion, and Meander Characterized by Sampling at Independent Uniform Times

For a random process X consider the random vector deened by the values of X at times 0 < U n;1 < ::: < U n;n < 1 and the minimal values of X on each of the intervals between consecutive pairs of these times, where the U n;i are the order statistics of n independent uniform (0; 1) variables, independent of X. The joint law of this random vector is explicitly described when X is a Brownian motion...

The maximal drawdown of the Brownian meander

Motivated by evaluating the limiting distribution of randomly biased random walks on trees, we compute the exact value of a negative moment of the maximal drawdown of the standard Brownian meander.

Analysis of Complex Brownian Functionals

Brownian penalisations related to excursion lengths, VII

Limiting laws, as t →∞, for Brownian motion penalised by the longest length of excursions up to t , or up to the last zero before t , or again, up to the first zero after t , are shown to exist, and are characterized. Résumé. Il est prouvé que les lois limites, lorsque t → ∞, du mouvement brownien pénalisé par la plus grande longueur des excursions jusqu’en t , ou bien jusqu’au dernier zéro ava...

Brownian Excursion Conditioned on Its Local Time