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

Enrico Bibbona1,3, Gianna Panfilo2 and Patrizia Tavella1

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The Ornstein–Uhlenbeck process is presented with its main mathematical properties and with original results on the first crossing times in the case of two threshold barriers. The interpretation of filtered white noise, its stationary spectrum and Allan variance are also presented for ease 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.


PACS

06.30.Ft Time and frequency

84.30.Vn Filters

05.40.Ca Noise

Subjects

Electronics and devices

Instrumentation and measurement

Statistical physics and nonlinear systems

Dates

Issue 6 (December 2008)

Received 16 July 2008

Published 5 December 2008



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