Volume 79, Number 6, September 2007
|Number of page(s)||5|
|Published online||21 August 2007|
Two-point correlation function of the fractional Ornstein-Uhlenbeck process
School of Physics and Astronomy, University of Leeds - LS2 9JT, UK
2 Institute for Theoretical Physics, University of Münster - Wilhelm-Klemm Str. 9, 48149 Münster, Germany
Accepted: 30 July 2007
We calculate the two-point correlation function for a subdiffusive continuous time random walk in a parabolic potential, generalizing well-known results for the single-time statistics to two times. A closed analytical expression is found for initial equilibrium, revealing non-stationarity and a clear deviation from a Mittag-Leffler decay. Our result thus provides a new criterion to assess whether a given stochastic process can be identified as a continuous time random walk.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.Fb – Random walks and Levy flights / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© Europhysics Letters Association, 2007
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