Two-point correlation function of the fractional Ornstein-Uhlenbeck processA. 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 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