Signal modeling with self-similar α-stable processes: the fractional Levy stable motion model

Kogon, S.M.; Manolakis, Dimitris G.

doi:10.1109/78.492557

Cited by 49 publications

(14 citation statements)

References 10 publications

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“…For this, we study the fractional Lévy motion (fLm) [41,43,42], which is analogous to fBm [20], with the Gaussian distribution of incre-ments replaced by a Lévy stable distribution. This corresponds to a moving average with infinite memory over a set of independent random variables having a Lévy distribution.…”

Section: Methods For Fractional Lévy Noise Synthesismentioning

confidence: 99%

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Zhou

Sornette

2002

Int. J. Mod. Phys. C

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We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) 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 non-Gaussian 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 false-alarm probability of the largest spectral peak of the Lomb periodogram in the presence of power-law distributed noises, of short-range and of long-range fractional-Gaussian noises. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the jointdistribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the second highest Lomb peak to the maximum peak. Using the insight obtained by the present statistical study, we re-examine previously reported claims of "log-periodicity" and find that the credibility for logperiodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

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Section: Methods For Fractional Lévy Noise Synthesismentioning

confidence: 99%

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Zhou

Sornette

2002

Int. J. Mod. Phys. C

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“…Stable interference modeling is used in many different fields, such as economics, physics, hydrology, biology, and electrical engineering [7], [8]. In communications, stable noise models have been verified experimentally in various underwater communications and radar applications [7]- [11].…”

Section: Introductionmentioning

confidence: 99%

Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers

Ilow

Hatzinakos

1998

IEEE Trans. Signal Process.

244

178

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This paper addresses non-Gaussian statistical modeling of interference as a superposition of a large number of small effects from terminals/scatterers distributed in the plane/volume according to a Poisson point process. This problem is relevant to multiple access communication systems without power control and radar. Assuming that the signal strength is attenuated over distance r r r as 1=r m 1=r m 1=r m , we show that the interference/clutter could be modeled as a spherically symmetric-stable noise. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted, such as the finite number of interferers and nonhomogeneous Poisson fields of interferers. In addition, the formulas derived allow us to predict noise statistics in environments with lognormal shadowing and Rayleigh fading. The results obtained are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws. Computer simulations are provided to demonstrate the efficiency of the stable noise model in multiuser communication systems. The analysis presented will be important in the performance evaluation of complex communication systems and in the design of efficient interference suppression techniques.

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“…are the arbitrary constants, + −1/ = 0 for ≤ 0 and + − 1 = − 1 etric Levy stable random measure, and is the self-similarity p ocess of fLsm [28] is as follows:…”

Section: X For Peer Reviewmentioning

confidence: 99%

“…is the symmetric Levy stable random measure, and H is the self-similarity parameter. The incremental process of fLsm [28] is as follows:…”

Section: Long-range Dependence and Self-similarity Fractional Levy Stmentioning

confidence: 99%

Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction

et al. 2020

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In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index α. Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by αH > 1.

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Signal modeling with self-similar α-stable processes: the fractional Levy stable motion model

Cited by 49 publications

References 10 publications

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Statistical Significance of Periodicity and Log-Periodicity With Heavy-Tailed Correlated Noise

Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers

Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction

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