Some measure-valued Markov processes attached to occupation times of Brownian motion
Donati-Martin, Catherine ; Yor, Marc
Bernoulli, Tome 6 (2000) no. 6, p. 63-72 / Harvested from Project Euclid
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We study the positive random measure $\Pi_t (\omega, \d y) = l_t^{B_t -y}\d y$ , where $(l^a_t; a \in \R, t > 0)$ denotes the family of local times of the one-dimensional Brownian motion B. We prove that the measure-valued process $(\Pi_t; t \geq 0) is a Markov process. We give two examples of functions $(f_i)_{i= 1, \dots, n}$ for which the process $(\Pi_t (f_i)_{i = 1, \dots, n}; t \geq 0)$ is a Markov process.
Publié le : 2000-02-14
Classification:  Brownian motion,  local times,  Markov processes 
@article{1082665380,
     author = {Donati-Martin, Catherine and Yor, Marc},
     title = {Some measure-valued Markov processes attached to occupation times of Brownian motion},
     journal = {Bernoulli},
     volume = {6},
     number = {6},
     year = {2000},
     pages = { 63-72},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082665380}
}

Donati-Martin, Catherine; Yor, Marc. Some measure-valued Markov processes attached to occupation times of Brownian motion. Bernoulli, Tome 6 (2000) no. 6, pp.  63-72. http://gdmltest.u-ga.fr/item/1082665380/