Reflected Brownian Motion

Reflected Brownian motion is a continuous-time continuous-state Markov process, which is constrained to its finite-dimensional state space S by a pushing mechanism on the boundary ∂S of S. In the context of Operations Research and Management Science, the state space S is typically the nonnegative orthant. This article reviews several aspects of reflected Brownian motion on this orthant: its construction, its positive recurrence, and its stationary distribution. Keywords: reflected Brownian motion; diffusion approximation; heavy traffic; positive recurrence; stationary distribution

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