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AN INTRODUCTION TO THE THEORY OF SELF-SIMILAR STOCHASTIC PROCESSES
International Journal of Modern Physics B, 2000 Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence.
EMBRECHTS, PAUL, MAEJIMA, MAKOTO
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Self-similar stochastic processes in solar wind turbulence
Advances in Space Research, 2008Abstract Solar wind data is used to estimate the autocorrelation function for the stochastic process x ( τ ) = y ( t + τ ) − y ( t ), considered as a function of τ , where y ( t ) is any one of the quantities B 2 ( t ), n p ( t ) V 2 ( t ), or n p ( t ).
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Governing stochastic equation for a self-similar random process
Physica A: Statistical Mechanics and its Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V.P. Koverda, V.N. Skokov
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Rotation algorithm: Generation of Gaussian self-similar stochastic processes
Physical Review E, 2012In this paper, we introduce a simple and practical method to generate Gaussian self-similar stochastic processes [fractional Gaussian noises (fGns) and fractional Brownian motions (fBms)] by interpolating between two known series of them. We apply the rotation algorithm to different cases including different pairs of fBms (fGns) and also different ...
M, Vahabi, G R, Jafari
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Estimation for time-changed self-similar stochastic processes
SPIE Proceedings, 2005We consider processes of the form X(t) = ˜ X( (t)) where ˜ X is a self-similar process with stationary increments andis a deterministic subordinator with a periodic activity function a = 0 > 0. Such processes have been proposed as models for high-frequency financial data, such as currency exchange rates, where there are known to be daily and weekly ...
W. Arroum, O.D. Jones
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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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A WAVELET METHOD COUPLED WITH QUASI-SELF-SIMILAR STOCHASTIC PROCESSES FOR TIME SERIES APPROXIMATION
International Journal of Wavelets, Multiresolution and Information Processing, 2011Scaling laws and generally self-similar structures are now well known facts in financial time series. Furthermore, these signals are characterized by the presence of stochastic behavior allowing their analysis with pure functional methods being incomplete.
Mohamed Essaied Hamrita +2 more
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Use of α-stable self-similar stochastic processes for modeling traffic in broadband networks
Performance Evaluation, 2000Summary: In this article, we propose a new model for aggregate network traffic. This model, besides reflecting self-similarity and long-range dependence, is able to capture the appropriate level of burstiness of different types of traffic by selecting the proper parameters.
José R. Gallardo +2 more
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Regression law of fluctuations and a self-similarity law of fractals in stochastic processes
Il Nuovo Cimento B Series 11, 1989By means of a new formulation of methods introduced in the theory of scaling expansion, it is shown that macroscopic laws and properties of fluctuations can be more easily determined. The main tool in this reformation is the use of a cumulant-generating function.
M. Ochiai, A. Holz, Y. Yamazaki, R. Ozao
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Self-similar stochastic processes with stationary increments as limits of particle systems
Stochastic Analysis and Applications, 2020We give a particle picture interpretation of two recently discovered classes of self-similar stable processes with stationary increments studied by Samorodnitsky et al.
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