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 IR sup N sub + 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 sup -1 b