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

We calculate the two-point correlation function < x((t)2) x(t(1))> 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-Leffer decay. Our result thus provides a new criterion to assess whether a given stochastic process can be identified as a continuous time random walk. Copyright (C) EPLA, 2007.