  We study the stationary reflected Brownian motion in a non-convex wedge,
which, compared to its convex analogue model, has been much rarely analyzed in
the probabilistic literature. We prove that its stationary distribution can be
found by solving a two dimensional vector boundary value problem (BVP) on a
single curve for the associated Laplace transforms. The reduction to this kind
of vector BVP seems to be new in the literature. As a matter of comparison, one
single boundary condition is sufficient in the convex case. When the parameters
of the model (drift, reflection angles and covariance matrix) are symmetric
with respect to the bisector line of the cone, the model is reducible to a
standard reflected Brownian motion in a convex cone. Finally, we construct a
one-parameter family of distributions, which surprisingly provides, for any
wedge (convex or not), one particular example of stationary distribution of a
reflected Brownian motion.
