Abstract
Consider an Ornstein–Uhlenbeck process with reflection at the origin. Such a process arises as an approximating process both for queueing systems with reneging or state-dependent balking and for multi-server loss models. Consequently, it becomes important to understand its basic properties. In this paper, we show that both the steady-state and transient behavior of the reflected Ornstein–Uhlenbeck process is reasonably tractable. Specifically, we (1) provide an approximation for its transient moments, (2) compute a perturbation expansion for its transition density, (3) give an approximation for the distribution of level crossing times, and (4) establish the growth rate of the maximum process.
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Ward, A.R., Glynn, P.W. Properties of the Reflected Ornstein–Uhlenbeck Process. Queueing Systems 44, 109–123 (2003). https://doi.org/10.1023/A:1024403704190
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DOI: https://doi.org/10.1023/A:1024403704190