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1977•The Annals of ProbabilityOpen access

Weak Convergence to Brownian Meander and Brownian Excursion

Richard Durrett, Donald L. Iglehart, Douglas R. Miller

Open full text 160 citations

Abstract

We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.

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We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.

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Available abstract

We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.

Key concepts: Meander (mathematics), Brownian excursion, Excursion, Brownian bridge, Brownian motion, Mathematics, Reflected Brownian motion, Geometric Brownian motion

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