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On the Aggregation of Self-Similar Processes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2005The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes.
MAZZINI, Gianluca +2 more
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Multifractal analysis of self-similar processes
2012 IEEE Statistical Signal Processing Workshop (SSP), 2012Scale invariance and multifractal analysis are nowadays widely used in applications. For modeling scale invariance in data, two classes of processes are classically in competition: self-similar processes and multiplicative cascades. They imply fundamentally different underlying (additive or multiplicative) mechanisms, hence the crucial practical need ...
Herwig Wendt +2 more
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Self-similar processes in communications networks
IEEE Transactions on Information Theory, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boris Tsybakov, Nicolas D. Georganas
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On wavelet compression of self-similar processes
Data Compression Conference, 2004. Proceedings. DCC 2004, 2004Self-similar stochastic processes are stochastic counterparts of deterministic fractals. Fractional Brownian motion (fBm) is a self-similar nonstationary Gaussian process originally proposed to model power-law behavior of power spectrum of long-range dependant (LRD) natural processes.
Nima Sarshar, Xiaolin Wu 0001
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On Lévy–Fréchet processes and related self-similar and semi-self-similar ones
Chaos, Solitons & Fractals, 2002Let \(X(t)\) be the Lévy subordinator of index ...
Huillet, Thierry, Ben Alaya, Mohamed
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On the Effect of Measuring a Self-Similar Process
SIAM Journal on Applied Mathematics, 1995Summary: There has been recent statistical interest in modelling irregular physical features by stochastic fractal processes and studying the statistical properties of the resulting estimators of fractal dimension. However, even if physical features were exactly fractal in character, the manner of recording those features would usually corrupt the self-
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Estimating the self-similar exponent of broad-sense self-similar processes
Physica A: Statistical Mechanics and its Applications, 2016Abstract In this paper, a new algorithm about the self-similar exponent of self-similar processes is introduced which is used to explore long memory in financial time series. This method can work for more general broad-sense self-similar processes. We prove that this algorithm performs much better than the classical methods.
Jing Zheng, Guijun Zhang, Changqing Tong
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SELF-SIMILARITY OF FREE STOCHASTIC PROCESSES
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006In this paper we study self-similarity of free stochastic processes. We establish the noncommutative counterpart of Lamperti's self-similar processes. We develop the characterization of noncommutative self-similar processes through a modification of Voiculescu transform, the free cumulant transform. We study the connection between free self-similarity,
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2016
The notion of self-similarity was already introduced in Section 3.5 Recall that a stochastic process \({\bigl (X(t),\,t \geq 0\bigr )}\) is called self ...
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The notion of self-similarity was already introduced in Section 3.5 Recall that a stochastic process \({\bigl (X(t),\,t \geq 0\bigr )}\) is called self ...
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Modeling of network traffic with self-similar process
Proceedings of the 9th International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing - CompSysTech '08, 2008This paper presents three algorithms for modelling of self-similar network traffic, based on the fractional Gaussian noise (FGN). These algorithms use different manners to compute the power spectrum of FGN. In the paper was made comparative analysis between them in terms of the computation speed and the accuracy in generating self-similar traffic with ...
Evgeniya Gospodinova, Mitko Gospodinov
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