测量初始瞬态：反射布朗运动
Measuring the Initial Transient: Reflected Brownian Motion
摘要：
本文分析了一维反射布朗运动（RBM）到平衡点的收敛性，并计算了一些相关的初始瞬态公式。这些公式是感兴趣的近似的初始瞬态的拥挤的交通系统，并帮助我们确定设置中的初始化偏差是显着的。最后，我们讨论了RBM的均方误差。我们的分析支持这样的观点，即RBM和相关模型的初始瞬态效应通常相对于内在随机变异性具有适度的大小，除非选择特别差的初始化。
英文摘要：
We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing systems in heavy traffic, and help us to identify settings in which initialization bias is significant. We conclude with a discussion of mean square error for RBM. Our analysis supports the view that initial transient effects for RBM and related models are typically of modest size relative to the intrinsic stochastic variability, unless one chooses an especially poor initialization.
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