Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T15:00:19.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications

Published online by Cambridge University Press:  14 July 2016

J.-P. Imhof
J.-P. Imhof*
Affiliation:
University of Geneva
*
∗Postal address: Section de Mathématiques, Case Postale 240, 1211 Geneva 24, Switzerland.
Get access Rights & Permissions [Opens in a new window]

Abstract

Joint densities concerning in particular the value and time of the maximum over a fixed time interval, or the behavior over intervals determined by some first- and last-passage times, are determined for Brownian motion, the three-dimensional Bessel process and Brownian meander. Simple change of measure formulas permit easy passage from one process to the other. Examples are given.

Keywords

MAXIMUMPASSAGE TIMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 500 - 510
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chung, K. L. (1976) Excursions in brownian motion. Ark. Mat. 14, 155–177.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Imhof, J. P. (1984) On Brownian bridge and excursion. Studia Sci. Math. Hungar. Google Scholar
Knight, F. (1969) Brownian local times and taboo processes. Trans. Amer. Math. Soc. 143, 173–185.CrossRefGoogle Scholar
Knight, F. (1980) On the excursion process of Brownian motion. Trans. Amer. Math. Soc. 258, 77–86.CrossRefGoogle Scholar
Knopp, K. (1947) Theorie und Anwendung der unendlichen Reihen, 4th edn. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Louchard, G. (1968) Mouvement brownien et valeurs propres du Laplacien. Ann. Inst. H. Poincaré (IV) 4, 331–342.Google Scholar
Louchard, G. (1984) Kac's formula, Lévy's local time and Brownian excursion. J. Appl. Prob. 21, 00000 CrossRefGoogle Scholar
Millar, P. W. (1977) Zero-one laws and the minimum of a Markov process. Trans. Amer. Math. Soc. 226, 365–391.CrossRefGoogle Scholar
Vincze, I. (1957) Einige zweidimensionale Verteilungs- und Grenzverteilungssätze in der Theorie der geordneten Stichproben. Publ. Math. Inst. Hungar. Acad. Sc. II, 183–203.Google Scholar
Wendel, J. G. (1980) Hitting spheres with Brownian motion. Ann. Prob. 8, 164–169.CrossRefGoogle Scholar
Williams, D. (1974) Path decomposition and continuity of local time for one-dimensional diffusions, I. Proc. London Math. Soc. 28, 738–768.CrossRefGoogle Scholar
Wei, Zhou Xing and Rong, Wu (1982) Some extreme theorems of Brownian motion. Dept. of Math. Nankai Univ., Tienjin.Google Scholar