Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 12 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081788033

Mathematical Reviews number (MathSciNet)
MR2001c:60062

Zentralblatt MATH identifier
0955.60074

Keywords
crossings diagram formula local time mixing processes

Citation

León, José R.; Perera, Gonzalo. Approximation of the Ornstein-Uhlenbeck local time by harmonic oscillators. Bernoulli 6 (2000), no. 2, 357--379. https://projecteuclid.org/euclid.bj/1081788033


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