Weak Convergence to Brownian Excursion

Weak Convergence of Reflecting Brownian Motions

1. Introduction. We will show that if a sequence of domains D k increases to a domain D then the reflected Brownian motions in D k 's converge to the reflected Brownian motion in D, under mild technical assumptions. Our theorem follows easily from known results and is perhaps known as a " folk law " among the specialists but it does not seem to be recorded anywhere in an explicit form. The purp...

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent...

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...

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...

Brownian Excursion Conditioned on Its Local Time