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1981•Canadian Journal of StatisticsRequires access

Excursion and meander in random walk

Endre Csáki, S. G. Mohanty

Open publisher page 24 citations

Abstract

Abstract Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge, excursion and meander (cf. Chung 1976). Distributions of certain characteristics defined on these Bernoulli processes, which are of a combinatorial nature, and their limits are obtained. Using weak convergence, these derivations give a verification of some of the earlier results on Brownian excursion and Brownian meander, as well as some new results.

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What this paper is about

Abstract Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge, excursion and meander (cf. Chung 1976). Distributions of certain characteristics defined on these Bernoulli processes, which are of a combinatorial nature, and their limits are obtained. Using weak convergence, these derivations give a verification of some of the earlier results on Brownian excursion and Brownian meander, as well as some new results.

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Available abstract

Abstract Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge, excursion and meander (cf. Chung 1976). Distributions of certain characteristics defined on these Bernoulli processes, which are of a combinatorial nature, and their limits are obtained. Using weak convergence, these derivations give a verification of some of the earlier results on Brownian excursion and Brownian meander, as well as some new results.

Key concepts: Meander (mathematics), Excursion, Brownian excursion, Brownian bridge, Brownian motion, Random walk, Bernoulli's principle, Mathematics

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