The Annals of Probability

Some Brownian functionals and their laws

C. Donati-Martin and M. Yor

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Abstract

We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob’s $h$-transforms of Brownian motion, for nonpositive harmonic functions $h$. We also give a survey and complement some martingale approaches to Ray–Knight theorems for local times.

Article information

Source
Ann. Probab. Volume 25, Number 3 (1997), 1011-1058.

Dates
First available in Project Euclid: 18 June 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1024404505

Digital Object Identifier
doi:10.1214/aop/1024404505

Mathematical Reviews number (MathSciNet)
MR1457611

Zentralblatt MATH identifier
0885.60072

Subjects
Primary: 60J55: Local time and additive functionals 60J60: Diffusion processes [See also 58J65] 60J65: Brownian motion [See also 58J65] 33C05: Classical hypergeometric functions, $_2F_1$

Keywords
Space-time harmonic functions principal values of local times Ray-Knight theorems generalized Bessel processes

Citation

Donati-Martin, C.; Yor, M. Some Brownian functionals and their laws. Ann. Probab. 25 (1997), no. 3, 1011--1058. doi:10.1214/aop/1024404505. http://projecteuclid.org/euclid.aop/1024404505.


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