TY  - JOUR
A1  - Mardoukhi, Yousof
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Spurious ergodicity breaking in normal and fractional Ornstein–Uhlenbeck process
JF  - New Journal of Physics
N2  - The Ornstein–Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein–Uhlenbeck process and its fractional extension. For the fractional Ornstein–Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition.
KW  - Ornstein–Uhlenbeck process
KW  - stationary stochastic process
KW  - ensemble and time averaged mean squared displacement
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab950b
SN  - 1367-2630
VL  - 22
PB  - IOP
CY  - London
ER  -