Note: Brownian motion of colloidal particles of arbitrary shape
  The analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is such that the rotational-rotational diffusion tensor is diagonal. 
Bogdan Cichocki, Maria L. Ekiel-Jezewska, Eligiusz Wajnryb
cond-mat.soft