A warning about an independence property related to random Brownian scaling

• Autorzy: Fujita T. , Yor M.
• Języki publikacji: EN

Abstrakty

EN

In this note, which develops a part of our paper [2], we consider independence properties between Brownian motion, after Brownian scaling on a random interval (a, b), and the length (b—a) of the interval. We indicate three examples for which the Brownian scaled process is independent of the corresponding length. On the other hand, we discuss a case where this independence property does not hold and investigate further results for that example.

Słowa kluczowe

EN

Standard Brownian motion; Brownian scaling; Excursion; last zero; first zero; Brownian meander; Bessel processes

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 1
• Strony: 105--108
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Fujita T.

• Graduate School of Commerce and Management, Hitotsubashi University, Naka 2.1, Kunitachi, Tokyo 186.8601 Japan

autor

Yor M.

• Laboratoire de Probabilités et Modeles Aléatoires Université, Paris VI easier 188,4, place Jussieu, 75 252 Paris cedex 05, France

Bibliografia

• [1] P. Biane and M. Yor, Quelques precisions sur le méandre brownien, Bull. Sei. Math. 112 (1988), pp. 101-109.
• [2] T. Fujita and M. Yor, On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian motion, this fascicle, pp. 89-104.
• [3] M. Yor, Some Aspects of Brownian Motion. Part I: Some Special Functionals, Lectures Math. ETH Zürich, Birkhäuser, 1992.
• [4] M. Yоr, Random Brownian scaling and some absolute continuity relationships, Progr. Probab. 36, E. Bolthausen, M. Dozzi and F. Russo (Eds.), Birkhäuser, 1995, pp. 243-252.