scholarly journals Evolution of the Power Spectrum and Self‐Similarity in the Expanding One‐dimensional Universe

1998 ◽  
Vol 118 (2) ◽  
pp. 267-274 ◽  
Author(s):  
Taihei Yano ◽  
Naoteru Gouda
Keyword(s):  
Power Spectrum ◽  
Self Similarity ◽  
One Dimensional

scholarly journals The one-dimensional Lyαforest power spectrum from BOSS

2013 ◽  
Vol 559 ◽  
pp. A85 ◽  
Author(s):  
Nathalie Palanque-Delabrouille ◽  
Christophe Yèche ◽  
Arnaud Borde ◽  
Jean-Marc Le Goff ◽  
Graziano Rossi ◽  
...  
Keyword(s):  
Power Spectrum ◽  
One Dimensional ◽  
The One

scholarly journals Interferometric Techniques Applied to High Resolution Observation of the Solar Granulation

1979 ◽  
Vol 50 ◽  
pp. 30-1-30-6
Author(s):  
Claude Aime
Keyword(s):  
High Resolution ◽  
Power Spectrum ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Solar Granulation ◽  
One Dimensional ◽  
Resolution Observation ◽  
Stellar Interferometry ◽  
High Resolution Observation

AbstractMichelson,one-dimensional, and two-dimensional apertures are used to obtain the statistical properties of the solar granulation. The calibration of the power spectrum is performed via Michelson stellar interferometry as well as by the use of changes in seeing conditions during speckle-interferometric measurements. The correction of 40 analyses, determined with Fried's parameter ro ranging between 2.5 cm and 11.5 cm, provides satisfactory convergence for frequencies up to 3 cycles per arc second

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 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.

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