  Time evolution of the position-velocity correlation functions (PVCF) plays a
key role in a new formalism of Brownian motion. A system of differential
equations, which governs PVCF, is derived for magnetic Skyrmions on a
2-dimensional magnetic thin film with thermal agitation. In the formalism, a
new type of diffusion coeffcient is introduced which does not come out in the
usual diffusion equations. The mean-square displacement (MSD) is obtained from
the PVCF and found that it oscillates in time when the damping constant is
small. It is also shown, even for a structureless particle, that the famous
Ornstein-Fuerth formula should be corrected taking a proper initial value of
PVCF into account.
