Bernoulli

Some measure-valued Markov processes attached to occupation times of Brownian motion

Catherine Donati-Martin and Marc Yor

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Abstract

We study the positive random measure Π t (ω,dy)=l t B t -ydy , where ( l t a;aR,t>0) denotes the family of local times of the one-dimensional Brownian motion B. We prove that the measure-valued process ( Π t;t0) is a Markov process. We give two examples of functions ( f i) i =1,...,n for which the process ( Π t(f i) i =1,...,n;t0) is a Markov process.

Article information

Source
Bernoulli, Volume 6, Number 1 (2000), 63-72.

Dates
First available in Project Euclid: 22 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1082665380

Mathematical Reviews number (MathSciNet)
MR2002f:60155

Zentralblatt MATH identifier
0956.60086

Keywords
Brownian motion local times Markov processes

Citation

Donati-Martin, Catherine; Yor, Marc. Some measure-valued Markov processes attached to occupation times of Brownian motion. Bernoulli 6 (2000), no. 1, 63--72. https://projecteuclid.org/euclid.bj/1082665380


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