Semimartingale reflecting Brownian motions: tail asymptotics for stationary distributions

Multidimensional semimartingale reflecting Brownian motions (SRBMs) arise as the diffusion limits for stochastic networks. I will describe a powerful methodology to obtain the tail asymptotics of the stationary distribution of an SRBM. The methodology uses a moment generating function version of the basic adjoint relationship that characterizes the stationary distribution. The tail asymptotics can be used to predict quality of service in stochastic networks. It can also be used to speed up an algorithm, devised in Dai and Harrison (1992), to compute the stationary distribution. This talk is based on joint works with Masakio Miyazawa and Jian Wu.