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

TL;DR

This paper derives an analytical expression for the two-point correlation function of a subdiffusive continuous time random walk in a parabolic potential, highlighting deviations from classical Mittag-Leffler decay in equilibrium.

Contribution

It extends the understanding of two-time statistics for fractional Ornstein-Uhlenbeck processes by providing a closed-form correlation function.

Findings

Analytical expression for two-point correlation function derived

Deviation from Mittag-Leffler decay observed in equilibrium

Results applicable to subdiffusive processes in confining potentials

Abstract

We calculate the two-point correlation function <x(t2)x(t1)> 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 a clear deviation from a Mittag-Leffler decay.