  We study rare event simulations of semimartingale reflecting Brownian motions
(SRBMs) in an orthant. The rare event of interest is that a $d$-dimensional
positive recurrent SRBM enters the set $B_n = \{z\in\mathbb{R}^d: \sum_{k=1}^d
z_k = n\}$ before reaching a small neighborhood of the origin as $n\to\infty$.
We show that under a proper scaling and some regularity conditions, the
probability of interest satisfies a large deviation principle. We then
construct a subsolution to the variational problem for our rare event, and
based on this subsolution construct particle based simulation algorithms to
estimate the probability of the rare event. It is shown that the proposed
algorithm is stable and theoretically superior to standard Monte Carlo for a
broad class of positive recurrent SRBMs.
