scholarly journals Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Junfeng Liu ◽  
Litan Yan ◽  
Zhihang Peng ◽  
Deqing Wang
Keyword(s):  
Brownian Motion ◽  
Confidence Intervals ◽  
The Self ◽  
Concentration Inequalities ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Convergence Results ◽  
Subfractional Brownian Motion ◽  
Quadratic Variations

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.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Multi-Feature Based Ocean Oil Spill Detection for Polarimetric SAR Data Using Random Forest and the Self-Similarity Parameter

2019 ◽  
Vol 11 (4) ◽  
pp. 451 ◽  
Author(s):  
Shengwu Tong ◽  
Xiuguo Liu ◽  
Qihao Chen ◽  
Zhengjia Zhang ◽  
Guangqi Xie
Keyword(s):  
Wind Speed ◽  
Random Forest ◽  
Oil Spill ◽  
The Self ◽  
Detection Accuracy ◽  
Self Similarity ◽  
Polarimetric Sar ◽  
Similarity Parameter ◽  
Oil Spill Detection ◽  
Sar Data

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°.

scholarly journals A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY

Fractals ◽  
2004 ◽  
Vol 12 (03) ◽  
pp. 331-346 ◽  
Author(s):  
SERGIO BIANCHI
Keyword(s):  
Necessary Conditions ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Probability Distribution Functions ◽  
Self Similar ◽  
The One ◽  
New Distribution

In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

scholarly journals On the Self-Intersection Local Time of Subfractional Brownian Motion

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Junfeng Liu ◽  
Zhihang Peng ◽  
Donglei Tang ◽  
Yuquan Cang
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Local Time ◽  
Noise Analysis ◽  
The Self ◽  
White Noise Analysis ◽  
Intersection Local Time ◽  
Subfractional Brownian Motion

We study the problem of self-intersection local time ofd-dimensional subfractional Brownian motion based on the property of chaotic representation and the white noise analysis.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (2) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Estimation of the self-similarity parameter in long memory processes

1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker
Keyword(s):  
Long Memory ◽  
The Self ◽  
Similar Process ◽  
Long Range Dependence ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Data Set ◽  
Memory Processes ◽  
Long Memory Processes ◽  
Self Similar

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  

Robust estimation of the self-similarity parameter in network traffic using wavelet transform

2007 ◽  
Vol 87 (9) ◽  
pp. 2111-2124 ◽  
Author(s):  
Haipeng Shen ◽  
Zhengyuan Zhu ◽  
Thomas C.M. Lee
Keyword(s):  
Wavelet Transform ◽  
Robust Estimation ◽  
Network Traffic ◽  
The Self ◽  
Self Similarity ◽  
Similarity Parameter

Estimation of the self-similarity parameter in linear fractional stable motion

2002 ◽  
Vol 82 (12) ◽  
pp. 1873-1901 ◽  
Author(s):  
Stilian Stoev ◽  
Vladas Pipiras ◽  
Murad S. Taqqu
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion
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