A Relation between Brownian Bridge and Brownian Excursion

An excursion approach to maxima of the Brownian bridge.

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivatio...

A"Burnt Bridge'' Brownian Ratchet

Motivated by a biased diffusion of molecular motors with the bias dependent on the state of the substrate, we investigate a random walk on a one-dimensional lattice that contains weak links (called " bridges ") which are affected by the walker. Namely, a bridge is destroyed with probability p when the walker crosses it; the walker is not allowed to cross it again and this leads to a directed mo...

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

Brownian Motion: The Link Between Probability and Mathematical Analysis

This article has no abstract.