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31
Statistical Significance of periodicity and logperiodicity with heavytailed correlated Noise
, 2001
"... We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or logperiodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general s ..."
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Cited by 15 (9 self)
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We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or logperiodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with nonGaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the falsealarm probability of the largest spectral peak of the Lomb periodogram in the presence of powerlaw distributed noises, of shortrange and of longrange fractionalGaussian noises. Increasing heavytailness (respectively correlations describing persistence) tends to decrease (respectively increase) the falsealarm probability of finding a large spurious Lomb peak. Increasing antipersistence tends to decrease the falsealarm probability. We also study the interplay between heavytailness and longrange correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should
GPS Schedulers and Gaussian Traffic
, 2002
"... This article considers Gaussian flows which are fed into a GPS (Generalized Processor Sharing) scheduler. The system is analyzed using a most probable path approach. This method gives quite good approximations for performance measures, like queue length distributions in the full range of queue level ..."
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Cited by 12 (1 self)
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This article considers Gaussian flows which are fed into a GPS (Generalized Processor Sharing) scheduler. The system is analyzed using a most probable path approach. This method gives quite good approximations for performance measures, like queue length distributions in the full range of queue levels. The approximations are based on the distinction whether it is more probable that an aggregated queue consists of traffic from one class only or whether it is a combination of several classes. The approximate queue length distribution for a specific flow is then calculated either using the Empty Buffer Approximation or the authors' Rough Full Link Approximation, respectively.
Challenges in Mobile Electronic Commerce
 Transactions and Database Dynamics. LNCSNr. 1773
, 2000
"... : Advances in wireless network technology and the continuously increasing number of users of hand held terminals make the latter an ideal channel for offering personalized services to mobile users and give pace to the rapid development of Mobile Electronic Commerce (MEC). MEC operates partially in a ..."
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Cited by 10 (3 self)
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: Advances in wireless network technology and the continuously increasing number of users of hand held terminals make the latter an ideal channel for offering personalized services to mobile users and give pace to the rapid development of Mobile Electronic Commerce (MEC). MEC operates partially in a different environment than Internet ECommerce due to the special characteristics and constraints of mobile terminals and wireless networks and the context, situations and circumstances that people use their handheld terminals. In this paper, we discuss challenges in electronic commerce transactions including designing new business models, applications and services. Keywords : Mobile Computing, Electronic Commerce, Business Models, Transactions. 1. Introduction Advances in wireless network technology and the continuously increasing number of users of hand held terminals make the latter an ideal channel for offering personalized services to mobile users and give pace to the rapid develop...
On spectral simulation of fractional Brownian motion
 Engrg. Inform. Sci
, 2003
"... This paper focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class ..."
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Cited by 8 (1 self)
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This paper focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class of approximate methods that are based on the spectral properties of fBm’s stationary incremental process, usually called fractional Gaussian noise (fGn). The main contribution is a proof of asymptotical exactness (in a sense that is made precise) of these spectral methods. Moreover, we establish the connection between the spectral simulation approach and a widely used method, originally proposed by Paxson, that lacked a formal mathematical justification. The insights enable us to evaluate the Paxson method in more detail. It is also shown that spectral simulation is related to the fastest known exact method. 1
Approximating some Volterra type stochastic integrals with applications to parameter estimation
 STOCHASTIC PROCESS APPL
"... We use a general representation of continuous Gaussian processes as the limit of a sequence of processes in the associated reproducing kernel Hilbert space, to Gaussian processes represented as Volterra type stochastic integrals with respect to Brownian motion, including the fractional Brownian moti ..."
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Cited by 8 (0 self)
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We use a general representation of continuous Gaussian processes as the limit of a sequence of processes in the associated reproducing kernel Hilbert space, to Gaussian processes represented as Volterra type stochastic integrals with respect to Brownian motion, including the fractional Brownian motion. As special cases of this representation we obtain for example, the KarhunenLove decomposition for standard Brownian motion and a wavelet representation for fractional Brownian motion. We also show how the representation can be used to estimate parameters. In particular we derive an estimator for the meanreverting parameter in an OrnsteinUhlenbeck process driven by a fractional Brownian motion. 1
Simulating Sample Paths of Linear Fractional Stable Motion
, 2004
"... An algorithm for generating sample paths of linear fractional stable motion (LFSM) is introduced. It is based on the approximation of LFSM by a linear process and exhibits low computational complexity. A detailed analysis of the error term involved in the approximation is provided, which in turn gu ..."
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Cited by 6 (1 self)
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An algorithm for generating sample paths of linear fractional stable motion (LFSM) is introduced. It is based on the approximation of LFSM by a linear process and exhibits low computational complexity. A detailed analysis of the error term involved in the approximation is provided, which in turn guides the user on selecting the size of the generated sequence.
Parameter estimation of geometrically sampled fractional Brownian motion
 In Proceedings of IEEE Infocom 2000
, 2000
"... Abstract — The parameter estimation of a traffic modelbasedonthe fractional Brownian motion (fBm) is studied. The model has three parameters: mean rate Ñ, variance parameter � and the Hurst parameter À. Explicit expressions for the maximum likelihood (ML) estimates �Ñ and � � in terms of À are given ..."
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Cited by 4 (0 self)
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Abstract — The parameter estimation of a traffic modelbasedonthe fractional Brownian motion (fBm) is studied. The model has three parameters: mean rate Ñ, variance parameter � and the Hurst parameter À. Explicit expressions for the maximum likelihood (ML) estimates �Ñ and � � in terms of À are given, as well as the expression for the loglikelihood function from which the estimate � À is obtained as the maximizing argument. A geometric sequence of sampling points, Ø � � « �, is introduced, which fits neatly to the selfsimilar property of the process and also reduces the number of samples needed to cover several time scales. It is shown that by a proper ‘descaling ’ the traffic process is stationary on this grid leading to a Toeplitztype covariance matrix. Approximations for the inverted covariance matrix and its determinant are introduced. The accuracy of the estimations is studied by simulations. Comparisons with estimates obtained with linear sampling and with the waveletbased AV estimator show that the geometrical sampling indeed improves the accuracy of the estimate � À with a given number of samples. I.
KOM ScenGen  The Swiss Army Knife for Simulation and Emulation Experiments
 In Proceedings of The International Workshop on Multimedia Interactive Protocols and Systems
, 2003
"... Multimedia networking involves complex collections of protocols, in particular protocols that support the inherent quality of service (QoS) requirements of multimedia applications. Most often analytical treatment falls short in being able to assess the overall system behaviour or performance. ..."
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Cited by 4 (0 self)
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Multimedia networking involves complex collections of protocols, in particular protocols that support the inherent quality of service (QoS) requirements of multimedia applications. Most often analytical treatment falls short in being able to assess the overall system behaviour or performance.