  In this paper, we consider a two-dimensional sticky Brownian motion. Sticky
Brownian motions can be viewed as time-changed semimartingale reflecting
Brownian motions, which find applications in many areas including queueing
theory and mathematical finance. For example, a sticky Brownian motion can be
used to model a storage system.with exceptional services. In this paper, we
focus on stationary distributions for sticky Brownian motions. The main results
obtained here include tail asymptotic properties in boundary stationary
distributions, marginal distributions, and joint distributions. The kernel
method, copula concept and extreme value theory are main tools used in our
analysis.
