Ornstein-Uhlenbeck processes indexed by the circle
Norris, J. R.
Ann. Probab., Tome 26 (1998) no. 1, p. 465-478 / Harvested from Project Euclid
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We consider the class of stationary, zero-mean Gaussian processes, indexed by the circle, satisfying a two-point Markov property and taking values in a vector bundle over the circle with given holonomy. We establish, subject to certain additional symmetry properties, a classification of all such processes. We then propose a construction of a Brownian motion of loops, in which these processes provide the infinitesimal increments.
Publié le : 1998-04-14
Classification:  Ornstein-Uhlenbeck process,  Brownian motin of loops,  Gaussian processes,  two-sided Markov property,  60G15,  58G32,  60J60 
@article{1022855640,
     author = {Norris, J. R.},
     title = {Ornstein-Uhlenbeck processes indexed by the circle},
     journal = {Ann. Probab.},
     volume = {26},
     number = {1},
     year = {1998},
     pages = { 465-478},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022855640}
}

Norris, J. R. Ornstein-Uhlenbeck processes indexed by the circle. Ann. Probab., Tome 26 (1998) no. 1, pp.  465-478. http://gdmltest.u-ga.fr/item/1022855640/