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

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.

6 pages, 2 figures; Journal's website can be found at http://www.epljournal.org

References in corpus (5)

• Langevin equations for continuous time Lévy flights
• Aging Correlation Functions for Blinking Nano-Crystals, and Other On - Off Stochastic Processes
• Joint Probability Distributions for a Class of Non-Markovian Processes
• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk
• Non-Poisson dichotomous noise: higher-order correlation functions and aging

Cited by in corpus (3)

• Subordinated diffusion and CTRW asymptotics
• Langevin formulation of a subdiffusive continuous time random walk in physical time
• Generalized Khinchin Theorem for a Class of Aging Processes