Reflected Brownian motion in a wedge : sum-of-exponential stationary densities:
Reflected Brownian motion (RBM) in a two-dimensional wedge is a
well-known stochastic process. With an appropriate drift, it is positive
recurrent and has a stationary distribution, and the invariant measure
is absolutely continuous with respect to Lebesgue measure. I will give
necessary and sufficient conditions for the stationary density to be
written as a finite sum of exponentials with linear exponents. Such
densities are a natural generalisation of the stationary density of
one-dimensional RBM. Using geometric ideas reminiscent of the reflection
principle, I will give an explicit formula for the density in such
cases, which can be written as a determinant. Joint work with Ton
Dieker.