Properties of the reflected Ornstein–Uhlenbeck process

AR Ward, PW Glynn - Queueing Systems, 2003 - Springer
Queueing Systems, 2003Springer
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 …
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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