• Bernoulli
  • Volume 6, Number 2 (2000), 357-379.

Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators

José R. León and Gonzalo Perera

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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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Bernoulli, Volume 6, Number 2 (2000), 357-379.

First available in Project Euclid: 12 April 2004

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crossings diagram formula local time mixing processes


León, José R.; Perera, Gonzalo. Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators. Bernoulli 6 (2000), no. 2, 357--379.

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