Stationary distributions for two-dimensional sticky Brownian motions: Exact tail asymptotics and extreme value distributions

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. In this paper,we focus on stationary distributions for sticky Brownian motions. Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions. The kernel method, copula concept and extreme value theory are the main tools used in our analysis.