The Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes

We study locally self-similar processes (LSSPs) in Silverman’s sense. By deriving the minimum mean-square optimal kernel within Cohen’s class counterpart of time–frequency representations, we obtain an optimal estimation for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of estimators is completely characterized in terms of kernels, so the optimal kernel minimizes the mean-square error of the estimation. We obtain the SIWS estimation for two cases: global and local, where in the local case, the kernel is allowed to vary with time and frequency. We also introduce two generalizations of LSSPs: the locally self-similar chirp process and the multicomponent LSSP, and obtain their optimal kernels. Finally, the performance and accuracy of the estimation is studied via simulation.     

Approximation to two independent Gaussian processes from a unique Lévy process and applications

Abstract

In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.     

自相似业务流下的服务质量保障

将来网络服务质量需要考虑网络业务流自有的自相似性对网络性能的影响,而传统的网络模型未考虑此因素。该文利用分数布郎运动模型,建立了一个网络模型,此模型考虑了业务流的自相似,以及聚类的特性,通过控制有效带宽,提高统计复用效率,并通过审核控制机制,提供网络服务。实验证明分数布郎运动模型能如实描述业务流特性,准确预测业务流的性能,能够最大限度地利用网络资源,提高服务质量,弥补原来网络排队模型的缺陷。     

A remark on self-similar processes with stationary increments

The upper bound of the parameter of self-similar processes with stationary increments is given in terms of the moment condition.     

Optimal covariance estimation of discrete-time locally self-similar processes in time-scale and ambiguity domains

This paper investigates the optimal estimate of the covariance function in the sense of mean-square of errors, for the class of discrete-time locally self-similar processes. The covariance function is estimated in time-scale and ambiguity domains. Since the class of estimators is completely characterized in terms of kernels, the problem is reduced to finding the optimal kernel, which is obtained in time-scale domain. Also, the optimal kernel is computed for two classes of discrete-time locally self-similar and locally self-similar chirp processes. Furthermore, it is shown that the proposed method gives more accurate estimate than the ordinary methods for non stationary processes.     

自相似业务流的有效带宽

给出了传统业务流的有效带宽的计算方法和基于自相似业务流的有效带宽的计算方法,分析了分组丢失率、带宽利用率与缓冲区大小之间的关系,指出了网络设计中根据有效带宽进行资源管理的优越性。仿真结果表明,对自相似业务流,基于自相似业务流的有效带宽的计算比基于短相关模型的有效带宽的计算能保证更好的服务质量。     

一类自相似集在顶点处上凸密度的上界估计

利用了最好形状的定义,上凸密度的定义与一个重要性质,开集条件及自相似集的自相似结构对一类cantor集自乘积在其顶点处的上凸密度上限进行了较好的估计。并将所得结论应用到了一个具体的cantor集自乘积的上凸密度上限估计的实例上。     

Characterization of discrete scale invariant Markov sequences

ABSTRACT

Some special sampling of discrete scale invariant (DSI) processes are presented to provide a multi-dimensional self-similar process in correspondence. By imposing Markov property we show that the covariance functions of such Markov DSI sequences are characterized by variance, and covariance of adjacent samples in the first scale interval. We also provide a theoretical method for estimating spectral density matrix of corresponding multi-dimensional self-similar Markov process. Some examples such as simple Brownian motion (sBm) with drift and scale invariant autoregressive model are presented and these properties are investigated. We present two new method to estimate Hurst parameter of DSI processes and apply them to some sBm and also to the SP500 indices for some period which has DSI property. We compare our estimates with the maximum-likelihood and rescaled range (R/S) method which are applied to the corresponding multi-dimensional self-similar processes.     

一类Cantor型集合交的分形结构

通过对一类Cantor型集合交的结构的分析 ,获得了不同位置的Cantor型集合交的Hausdorff测度之间的关系 ,并进一步验证了关于它的维数公式 ,最后得到了这种交集合的Hausdorff测度的一个较好上界估计     

统计自相似测度的分形性质

对于一种利用可测映射序列构造的统计自相似集和统计自相似测度，得到了统计自相似测度的支撑集，以及统计自相似集关于统计自相似测度的0－1律性质．