Linear fractional stable motion: A wavelet estimator of the parameter

2012 ◽  
Vol 82 (8) ◽  
pp. 1569-1575 ◽  
Author(s):  
Antoine Ayache ◽  
Julien Hamonier
Keyword(s):  
Wavelet Estimator ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion

A novel crowd flow model based on linear fractional stable motion

2016 ◽  
Vol 30 (09) ◽  
pp. 1650049 ◽  
Author(s):  
Juan Wei ◽  
Hong Zhang ◽  
Zhenya Wu ◽  
Junlin He ◽  
Yangyong Guo
Keyword(s):  
Flow Rate ◽  
Flow Model ◽  
Threshold Value ◽  
Evacuation Time ◽  
Indoor Space ◽  
Stable Motion ◽  
Crowd Density ◽  
Linear Fractional Stable Motion ◽  
Positive Correlations ◽  
Fractional Stable Motion

For the evacuation dynamics in indoor space, a novel crowd flow model is put forward based on Linear Fractional Stable Motion. Based on position attraction and queuing time, the calculation formula of movement probability is defined and the queuing time is depicted according to linear fractal stable movement. At last, an experiment and simulation platform can be used for performance analysis, studying deeply the relation among system evacuation time, crowd density and exit flow rate. It is concluded that the evacuation time and the exit flow rate have positive correlations with the crowd density, and when the exit width reaches to the threshold value, it will not effectively decrease the evacuation time by further increasing the exit width.

scholarly journals Scaling Properties of the Empirical Structure Function of Linear Fractional Stable Motion and Estimation of Its Parameters

2014 ◽  
Vol 158 (1) ◽  
pp. 105-119 ◽  
Author(s):  
Danijel Grahovac ◽  
Nikolai N. Leonenko ◽  
Murad S. Taqqu
Keyword(s):  
Structure Function ◽  
Scaling Properties ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion

SIMULATION METHODS FOR LINEAR FRACTIONAL STABLE MOTION AND FARIMA USING THE FAST FOURIER TRANSFORM

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 95-121 ◽  
Author(s):  
STILIAN STOEV ◽  
MURAD S. TAQQU
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Moving Average ◽  
Approximation Error ◽  
Telecommunication Networks ◽  
Stable Motion ◽  
Riemann Sum ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion

We present efficient methods for simulation, using the Fast Fourier Transform (FFT) algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely, (i) the linear fractional stable motion (LFSM) process and (ii) the fractional autoregressive moving average (FARIMA) time series with SαS innovations. These two types of heavy-tailed processes have infinite variances and long-range dependence and they can be used in modeling the traffic of modern computer telecommunication networks. We generate paths of the LFSM process by using Riemann-sum approximations of its SαS stochastic integral representation and paths of the FARIMA time series by truncating their moving average representation. In both the LFSM and FARIMA cases, we compute the involved sums efficiently by using the Fast Fourier Transform algorithm and provide bounds and/or estimates of the approximation error. We discuss different choices of the discretization and truncation parameters involved in our algorithms and illustrate our method. We include MATLAB implementations of these simulation algorithms and indicate how the practitioner can use them.

Stochastic properties of the linear multifractional stable motion

2004 ◽  
Vol 36 (04) ◽  
pp. 1085-1115 ◽  
Author(s):  
Stilian Stoev ◽  
Murad S. Taqqu
Keyword(s):  
Sufficient Conditions ◽  
Infinite Variance ◽  
Regularity Conditions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Motion Process ◽  
Self Similar ◽  
Fractional Stable Motion

We study a family of locally self-similar stochastic processes Y = {Y(t)} t∈ℝ with α-stable distributions, called linear multifractional stable motions. They have infinite variance and may possess skewed distributions. The linear multifractional stable motion processes include, in particular, the classical linear fractional stable motion processes, which have stationary increments and are self-similar with self-similarity parameter H. The linear multifractional stable motion process Y is obtained by replacing the self-similarity parameter H in the integral representation of the linear fractional stable motion process by a deterministic function H(t). Whereas the linear fractional stable motion is always continuous in probability, this is not in general the case for Y. We obtain necessary and sufficient conditions for the continuity in probability of the process Y. We also examine the effect of the regularity of the function H(t) on the local structure of the process. We show that under certain Hölder regularity conditions on the function H(t), the process Y is locally equivalent to a linear fractional stable motion process, in the sense of finite-dimensional distributions. We study Y by using a related α-stable random field and its partial derivatives.

scholarly journals Linear Fractional Stable Motion with the rlfsm R Package

The R Journal ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 386
Author(s):  
Stepan Mazur ◽  
Dmitry Otryakhin
Keyword(s):  
R Package ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion

scholarly journals Estimation of the linear fractional stable motion

Bernoulli ◽  
2020 ◽  
Vol 26 (1) ◽  
pp. 226-252 ◽  
Author(s):  
Stepan Mazur ◽  
Dmitry Otryakhin ◽  
Mark Podolskij
Keyword(s):  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Fractional Stable Motion

scholarly journals Fourier Series Approximation of Linear Fractional Stable Motion

2008 ◽  
Vol 14 (2) ◽  
pp. 180-202 ◽  
Author(s):  
Hermine Biermé ◽  
Hans-Peter Scheffler
Keyword(s):  
Fourier Series ◽  
Stable Motion ◽  
Series Approximation ◽  
Linear Fractional Stable Motion ◽  
Fourier Series Approximation ◽  
Fractional Stable Motion

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

scholarly journals A minimal contrast estimator for the linear fractional stable motion

2020 ◽  
Vol 23 (2) ◽  
pp. 381-413
Author(s):  
Mathias Mørck Ljungdahl ◽  
Mark Podolskij
Keyword(s):  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Minimal Contrast ◽  
Fractional Stable Motion
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