If you need an accessible version of this item please contact JSTOR User Support

A Relation between Brownian Bridge and Brownian Excursion

Wim Vervaat
The Annals of Probability
Vol. 7, No. 1 (Feb., 1979), pp. 143-149
Stable URL: http://www.jstor.org/stable/2242845
Page Count: 7
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
A Relation between Brownian Bridge and Brownian Excursion
Preview not available

Abstract

It is shown that Brownian excursion is equal in distribution to Brownian bridge with the origin placed at its absolute minimum. This explains why the maximum of Brownian excursion and the range of Brownian bridge have the same distribution, a fact which was discovered by Chung and Kennedy. The result is proved by establishing similar relations for "Bernoulli excursions" and "Bernoulli bridges" constructed from symmetric Bernoulli walks, and exploiting known weak convergence results. Some technical complications arise from the fact that Bernoulli bridges assume their minimum value with positive probability more than once.

Page Thumbnails

  • Thumbnail: Page 
143
    143
  • Thumbnail: Page 
144
    144
  • Thumbnail: Page 
145
    145
  • Thumbnail: Page 
146
    146
  • Thumbnail: Page 
147
    147
  • Thumbnail: Page 
148
    148
  • Thumbnail: Page 
149
    149