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Science China Mathematics 2013年第11期56卷 2353-2366页

作者： WANG DingCheng Center of Financial Engineering Nanjing Audit University School of Mathematical Science University of Electronic Science and Technology of China

In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.

关键词： activity time asset pricing model asymptotical self-similarities gamma process inverse-gammaprocess L4vy process long-range dependence subordinator

Admission control with long-range dependence traffic input

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Journal of Harbin Institute of Technology(New Series) 2005年第4期12卷 396-399页

作者：饶云华邹雪城 School of Electronics Information Wuhan University Wuhan 430079 China Dept. of Electronics Science and Technology Huazhong Univ. of Science and Technology Wuhan 430074 China

The admission control scheme is investigated for a FIFO self-similar queuing system with Quality of Service (QoS) performance guarantees. Since the self-similar queuing system performance analysis is often carried out under the condition of infinite buffer, it is difficult to deduce the upper boundary of buffer overflow probability. To overcome this shortcoming, a simple overflow condition is proposed, which defines a buffer overflow occurrence whenever the arrival rate exceeds the service rate. The analytic formula for the buffer overflow probability upper boundary is easily obtained under this condition. The required bandwidth upper boundary with long-range dependence input and determined overflow probability is then derived from this formula. Based on the above analytic formulas, the upper boundaries of the admission control regions for homogeneous and heterogeneous long-range dependence traffic sources are separately obtained. Finally, an effective admission control scheme for long-range dependence input is proposed. Simulation studies with real traffic have confirmed the validity of these results.

关键词： long-range dependence queuing system overflow probability admission control

Stochastic process-based degradation modeling and RUL prediction: from Brownian motion to fractional Brownian motion

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Science China(Information Sciences) 2021年第7期64卷 5-24页

作者： Hanwen ZHANG Maoyin CHEN Jun SHANG Chunjie YANG Youxian SUN School of Automation and Electrical Engineering University of Science and Technology Beijing State Key Laboratory of Industrial Control Technology College of Control Science and EngineeringZhejiang University Department of Automation Tsinghua University School of Automation and Electrical Engineering Linyi University Department of Electrical and Computer Engineering University of Alberta

Brownian motion(BM) has been widely used for degradation modeling and remaining useful life(RUL) prediction, but it is essentially Markovian. This implies that the future state in a BM-based degradation process relies only on its current state, independent of the past states. However, some practical industrial devices such as Li-ion batteries, ball bearings, turbofans, and blast furnace walls show degradations with long-range dependence(LRD), where the future degradation states depend on both the current and past degradation states. This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs. Recently, in contrast to the work that uses only BM, fractional Brownian motion(FBM) is introduced to model practical degradations. The most important feature of the FBM-based degradation models is the ability to characterize the non-Markovian degradations with LRD. Although FBM is an extension of BM, it is neither a Markovian process nor a semimartingale. Therefore, how to obtain the first passage time of an FBM-based degradation process has become a challenging task. In this paper, a review of the transition of RUL prediction from BM to FBM is provided. The peculiarities of FBM when addressing the LRD inherent in some practical degradations are discussed. We first review the BM-based degradation models of the past few decades and then give details regarding the evolution of FBM-based research. Interestingly, the existing BM-based models scarcely consider the effect of LRD on the prediction of RULs. Two practical cases illustrate that the newly developed FBMbased models are more generalized and suitable for predicting RULs than the BM-based models, especially for degradations with LRD. Along with the direction of FBM-based RUL prediction, we also introduce some important and interesting problems that require further study.

关键词： remaining useful life degradation model Brownian motion fractional Brownian motion long-range dependence

WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH long MEMORY DATA

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Applied Mathematics and Mechanics(English Edition) 2006年第7期27卷 901-910页

作者：李林元肖益民 Department of Mathematics and Statistics University of New Hampshire 03824 USA Department of Statistics and Probability Michigan State University 48824 USA

This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel ***, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

关键词： nonlinear wavelet-based estimator nonparametric regression long-range dependence

Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process

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The Journal of China Universities of Posts and Telecommunications 2006年第3期13卷 61-64页

作者： ZHANG Di ZHANG Min YE Pei-da Key Laboratory of Optical Communications and Lightwave Technologies Beijing University of Posts and Telecommunications Beijing 100876 China

This article explores the short-range dependence （SRD） and the long-range dependence （LRD） of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process （FBNDP） model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity, the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity, and the effect of SRD.

关键词： fractal-binomial-noise-driven Poisson process short-range dependence long-range dependence self similarity

ARMA–GARCH model with fractional generalized hyperbolic innovations

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Financial Innovation 2022年第1期8卷 1407-1431页

作者： Sung Ik Kim Department of Economics and Finance College of BusinessLouisiana State University ShreveportOne University PlaceShreveportLA 71115USA

In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is *** define the fractional generalized hyperbolic process,the non-fractional variant is derived by subordinating time-changed Brownian motion to the generalized inverse Gaussian process,and thereafter,the fractional generalized hyperbolic process is obtained using the Volterra *** on the ARMA–GARCH model with standard normal innovations,the parameters are estimated for the high-frequency returns of six ***,the residuals extracted from the estimated ARMA–GARCH parameters are fitted to the fractional and non-fractional generalized hyperbolic *** results show that the fractional generalized hyperbolic process performs better in describing the behavior of the residual process of high-frequency returns than the non-fractional processes considered in this study.

关键词： Generalized hyperbolic process Time-changed Brownian motion long-range dependence Fractional Brownian motion ARMA-GARCH model

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American Journal of Computational Mathematics 2016年第1期6卷 17-22页

作者： Pushpalatha Sarla Mallikarjuna Reddy Doodipala Manohar Dingari Department of Engineering Mathematics GITAM University Hyderabad Campus Hyderabad India

The paper focuses on measuring self-similarity using few techniques by an index called Hurst index which is a self-similarity parameter. It has been evident that Internet traffic exhibits self-similarity. Motivated by this fact, real time web users at various centers considered here as traffic and it has been examined by various methods to test the self-similarity. The results from the experiments carried out verify that the traffic examined in the present study is self similar using a new method based on some descriptive measures;for example percentiles have been applied to compute Hurst parameter which gives intensity of the self-similarity. Numerical results and analysis we discussed and presented here play a significant role to improve the services at web centers in the view of quality of service (QOS).

关键词： long-range dependence Self-Similarity Poisson Process Percentiles Hurst Parameter

A New Procedure to Test for Fractional Integration

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Open Journal of Statistics 2016年第4期6卷 651-666页

作者： William Rea Chris Price Les Oxley Marco Reale Jennifer Brown Department of Economics and Finance University of Canterbury Christchurch New Zealand Department of Mathematics and Statistics University of Canterbury Christchurch New Zealand Waikato Management School University of Waikato Hamilton New Zealand

It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing between a null hypothesis of unifractal fractionally integrated processes and an alternative hypothesis of other processes which display the long memory property. The procedure is based on a pair of empirical, but consistently defined, statistics namely the number of breaks reported by Atheoretical Regression Trees (ART) and the range of the Empirical Fluctuation Process (EFP) in the CUSUM test. The new procedure establishes through simulation the bivariate distribution of the number of breaks reported by ART with the CUSUM range for simulated fractionally integrated series. This bivariate distribution is then used to empirically construct a test which rejects the null hypothesis for a candidate series if its pair of statistics lies on the periphery of the bivariate distribution determined from simulation under the null. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average and show that the rejection rate of the null is higher than if either statistic was used as a univariate test.

关键词： long-range dependence Strong dependence Global dependence Regression Trees CUSUM Test Volatility