A time-reversed representation for the tail probabilities of stationary reflected Brownian motion

We consider the exponential decay rate of the stationary tail probabilities of reflected Brownian motion X in the N-dimensional orthant having drift b, covariance matrix A, and constraint matrix D. Suppose that the Skorokhod or reflection mapping associated with the matrix D is well-defined and Lipschitz continuous on the space of continuous functions. Under the stability condition D-1bReflected Brownian motion Large deviations Rate function Stationary distribution Tail probabilities Cyclic trajectories Skew symmetry Product form Skorokhod Map Skorokhod Problem Optimal control Time-reversal Variational problem Single-class networks Feedforward networks Buffer overflow