Volume 79, Number 6, September 2007
Article Number 60004
Number of page(s) 5
Section General
Published online 21 August 2007
EPL, 79 (2007) 60004
DOI: 10.1209/0295-5075/79/60004

Two-point correlation function of the fractional Ornstein-Uhlenbeck process

A. Baule1 and R. Friedrich2

1  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

received 2 June 2007; accepted in final form 30 July 2007; published September 2007
published online 21 August 2007

We calculate the two-point correlation function $\langle x(t_{2})x(t_{1})\rangle $ 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.

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