  Sticky Brownian motions, as time-changed semimartingale reflecting Brownian
motions, have various applications in many fields, including queuing theory and
mathematical finance. In this paper, we are concerned about the stationary
distributions of a multidimensional sticky Brownian motion, provided it is
stable. We will study the large deviations principle for stationary
distribution and the tail behaviour of the joint stationary distribution.
