Wavelet based estimator for the self-similarity parameter of /spl alpha/-stable processes

Author(s):  
P. Abry ◽  
L. Delbeke ◽  
P. Flandrin
2013 ◽  
Vol 392 (21) ◽  
pp. 5330-5345 ◽  
Author(s):  
M. Fernández-Martínez ◽  
M.A. Sánchez-Granero ◽  
J.E. Trinidad Segovia

2019 ◽  
Vol 11 (4) ◽  
pp. 451 ◽  
Author(s):  
Shengwu Tong ◽  
Xiuguo Liu ◽  
Qihao Chen ◽  
Zhengjia Zhang ◽  
Guangqi Xie

Synthetic aperture radar (SAR) is an important means to detect ocean oil spills which cause serious damage to the marine ecosystem. However, the look-alikes, which have a similar behavior to oil slicks in SAR images, will reduce the oil spill detection accuracy. Therefore, a novel oil spill detection method based on multiple features of polarimetric SAR data is proposed to improve the detection accuracy in this paper. In this method, the self-similarity parameter, which is sensitive to the randomness of the scattering target, is introduced to enhance the discrimination ability between oil slicks and look-alikes. The proposed method uses the Random Forest classification combing self-similarity parameter with seven well-known features to improve oil spill detection accuracy. Evaluations and comparisons were conducted with Radarsat-2 and UAVSAR polarimetric SAR datasets, which shows that: (1) the oil spill detection accuracy of the proposed method reaches 92.99% and 82.25% in two datasets, respectively, which is higher than three well-known methods. (2) Compared with other seven polarimetric features, self-similarity parameter has the better oil spill detection capability in the scene with lower wind speed close to 2–3 m/s, while, when the wind speed is close to 9–12 m/s, it is more suitable for oil spill detection in the downwind scene where the microwave incident direction is similar to the sea surface wind direction and performs well in the scene with incidence angle range from 29.7° to 43.5°.


2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Junfeng Liu ◽  
Litan Yan ◽  
Zhihang Peng ◽  
Deqing Wang

We first present two convergence results about the second-order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self-similarity parameter associated with one-dimensional subfractional Brownian motion.


1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation. Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise. DOI: 10.3329/jme.v38i0.898 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37  


2021 ◽  
Vol 244 ◽  
pp. 07002
Author(s):  
Tatiana Tatarnikova ◽  
Igor Sikarev ◽  
Vladimir Karetnikov ◽  
Artem Butsanets

The self-similarity properties of the considered traffic were checked on different time scales obtained on the available daily traffic data. An estimate of the tail severity of the distribution self-similar traffic was obtained by constructing a regression line for the additional distribution function on a logarithmic scale. The self-similarity parameter value, determined by the severity of the distribution “tail”, made it possible to confirm the assumption of traffic self-similarity. A review of models simulating real network traffic with a self-similar structure was made. Implemented tools for generating artificial traffic in accordance with the considered models. Made comparison of artificial network traffic generators according to the least squares method criterion for approximating the artificial traffic point values by the approximation function of traffic. Qualitative assessments traffic generators in the form of the software implementation complexity were taken into account, which, however, can be a subjective assessment. Comparative characteristics allow you to choose some generators that most faithfully simulate real network traffic. The proposed sequence of methods to study the network traffic properties is necessary to understand its nature and to develop appropriate models that simulate real network traffic.


2019 ◽  
Vol 204 ◽  
pp. 01021 ◽  
Author(s):  
Alexander Malakhov ◽  
Gennady Lykasov

It is shown that the inclusive spectra of the produced hadrons in hadron-hadron and nuclear-nuclear collisions can be presented as the universal function dependent of the self-similarity parameter in the analytical form. The article gives a description of the self-similarity parameter depending on the rapidity in the mid-rapidity region. The experimental data are in good agreement with the results of our calculations in a wide energy range from a few GeV to a few TeV in the central rapidity region.


2014 ◽  
Vol 42 (1) ◽  
pp. 398-430 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Juan Carlos Pardo ◽  
Alexander R. Watson

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