Journal ArticleDOI
Fractional Brownian Motions, Fractional Noises and Applications
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This article is published in Siam Review.The article was published on 1968-10-01. It has received 7199 citations till now. The article focuses on the topics: Fractional Brownian motion & Diffusion process.read more
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
On the self-similar nature of Ethernet traffic (extended version)
TL;DR: It is demonstrated that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, and that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks.
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An introduction to long‐memory time series models and fractional differencing
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
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The estimation and application of long memory time series models
John Geweke,Susan Porter-Hudak +1 more
TL;DR: In this article, a new estimator of the long memory parameter in these models is proposed, based on the simple linear regression of the log periodogram on a deterministic regressor.
References
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Journal ArticleDOI
Statistical Theory of Turbulence
TL;DR: In this paper, the scale of turbulence is defined in terms of the correlation between the velocity of a particle at one time and that of the same particle at a later time, or between simultaneous velocities at two fixed points.
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The Asymptotic Distribution of the Range of Sums of Independent Random Variables
TL;DR: In this paper, the asymptotic distribution of the range and normalized range of the sum of $n$ independent variables is derived using the theory of Brownian motion, which is a well-known technique in statistical analysis.
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Semi-stable stochastic processes
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The Typical Spectral Shape of an Economic Variable
TL;DR: In this article, a number of power spectra have been estimated from economic data and the majority have been found to be of a similar shape, and the implications of this shape are discussed, particular attention being paid to the reality of business cycles, stability and control problems, and model building.