无限源泊松过程记忆参数的估计
Estimation of the Memory Parameter of the Infinite Source Poisson Process
摘要：
由重尾引起的长程相关性是互联网流量的一个广泛报道的特征。长期相关性可以定义为积分过程方差的规则变化，规则变化指数的一半称为赫斯特指数。无限源泊松过程（$M/G/\infty$队列是它的一个特例）是一个简单而流行的具有这种性质的模型，当服务时间分布的尾部是有规律地变化时.无限源泊松过程的Hurst指数与服务时间的规则变化指数有关。在本文中，我们提出了一个基于小波的估计的赫斯特指数的这个过程中，当它被观察到连续或离散在一个增加的时间间隔。我们的估计被证明是一致的和强大的某种形式的非平稳性。研究了它的收敛速率。
英文摘要：
Long-range dependence induced by heavy tails is a widely reported feature of internet traffic. Long-range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of regular variation is then referred to as the Hurst index. The infinite-source Poisson process (a particular case of which is the $M/G/\infty$ queue) is a simple and popular model with this property, when the tail of the service time distribution is regularly varying. The Hurst index of the infinite-source Poisson process is then related to the index of regular variation of the service times. In this paper, we present a wavelet-based estimator of the Hurst index of this process, when it is observed either continuously or discretely over an increasing time interval. Our estimator is shown to be consistent and robust to some form of non-stationarity. Its rate of convergence is investigated.
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