Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: application to postural sway.
We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.
Frank
T D
TD
Faculty of Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands.
Daffertshofer
A
A
Beek
P J
PJ
D000465:Algorithms; D017276:Friction; D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D011187:Posture; D013269:Stochastic Processes