The Ornstein–Uhlenbeck process as a model of a low pass filtered white noise

Abstract

The Ornstein-Uhlenbeck process is presented with its main mathematical properties and with original results on the first crossing times in case of two threshold barriers.The interpretation as filtered white noise, its stationary spectrum, and Allan variance are also presented for easiness of use in the time and frequency metrology field.An improved simulation scheme for the evaluation of first passage times between two barriers is also introduced.