Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators

León, José R.; Perera, Gonzalo

Bernoulli, Tome 6 (2000) no. 6, p. 357-379 / Harvested from Project Euclid

Résumé

We consider a particle of mass 1/β submitted to the action of an harmonic oscillator. If we add a white-noise external force, it is well known that the trajectories of the particle, for β tending to infinity, converge to an Ornstein-Uhlenbeck process. Using the number of crossings of the particle with a fixed level u, we construct a consistent estimator of the Ornstein-Uhlenbeck local time, giving an estimate of the speed of this convergence.

Publié le : 2000-04-14
Classification: crossings, diagram formula, local time, mixing processes

@article{1081788033,
     author = {Le\'on, Jos\'e R. and Perera, Gonzalo},
     title = {Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators},
     journal = {Bernoulli},
     volume = {6},
     number = {6},
     year = {2000},
     pages = { 357-379},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1081788033}
}

León, José R.; Perera, Gonzalo. Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators. Bernoulli, Tome 6 (2000) no. 6, pp.  357-379. http://gdmltest.u-ga.fr/item/1081788033/