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April 2000 Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators
José R. León, Gonzalo Perera
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Bernoulli 6(2): 357-379 (April 2000).


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.


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José R. León. Gonzalo Perera. "Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators." Bernoulli 6 (2) 357 - 379, April 2000.


Published: April 2000
First available in Project Euclid: 12 April 2004

zbMATH: 0955.60074
MathSciNet: MR2001C:60062

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability


Vol.6 • No. 2 • April 2000
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