Conditional law and occupation times of two-sided sticky Brownian motion

Sticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent exponential time and at a fixed time t > 0. As a classical problem, we find the distribution of the occupation times of a half-line, and at 0, which is the sticky point for the process. (C) 2020 Elsevier B.V. All rights reserved.