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

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