  We present the first exact simulation method for multidimensional reflected
Brownian motion (RBM). Exact simulation in this setting is challenging because
of the presence of correlated local-time-like terms in the definition of RBM.
We apply recently developed so-called $\varepsilon-$strong simulation
techniques (also known as Tolerance-Enforced Simulation) which allow us to
provide a piece-wise linear approximation to RBM with $\varepsilon $
(deterministic) error in uniform norm. A novel conditional acceptance/rejection
step is then used to eliminate the error. In particular, we condition on a
suitably designed information structure so that a feasible proposal
distribution can be applied.
