  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.
