scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (extended version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
Extended Version ◽  
One Dimensional ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (renewed version-2)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
One Dimensional ◽  
Temporal Series ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (renewed version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
One Dimensional ◽  
Temporal Series ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

A study on the variations in long-range dependence of solar energetic particles during different solar cycles

2018 ◽  
Vol 13 (S340) ◽  
pp. 47-48
Author(s):  
V. Vipindas ◽  
Sumesh Gopinath ◽  
T. E. Girish
Keyword(s):  
Long Range ◽  
Long Memory ◽  
Hurst Exponent ◽  
High Energy ◽  
Energetic Particles ◽  
Solar Energetic Particles ◽  
Long Range Dependence ◽  
Solar Cycles ◽  
Self Similarity ◽  
High Energy Particles

AbstractSolar Energetic Particles (SEPs) are high-energy particles ejected by the Sun which consist of protons, electrons and heavy ions having energies in the range of a few tens of keVs to several GeVs. The statistical features of the solar energetic particles (SEPs) during different periods of solar cycles are highly variable. In the present study we try to quantify the long-range dependence (or long-memory) of the solar energetic particles during different periods of solar cycle (SC) 23 and 24. For stochastic processes, long-range dependence or self-similarity is usually quantified by the Hurst exponent. We compare the Hurst exponent of SEP proton fluxes having energies (>1MeV to >100 MeV) for different periods, which include both solar maximum and minimum years, in order to find whether SC-dependent self-similarity exist for SEP flux.

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.

Long-Range Dependence of Traffic Flow and Speed of a Motorway: Dynamics and Correlation with Historical Incidents

2017 ◽  
Vol 2616 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Sai Chand ◽  
Gregory Aouad ◽  
Vinayak V. Dixit
Keyword(s):  
Time Series ◽  
Long Range ◽  
Traffic Congestion ◽  
Hurst Exponent ◽  
Fractal Theory ◽  
Urban Traffic ◽  
Spatial And Temporal Variation ◽  
Long Range Dependence ◽  
Incident Rates ◽  
Sydney Australia

Speed and flow of vehicles tend to have several effects on the dynamics of a transport system. Fluctuations of these variables can implicate congestion, can lower predictability, and may even catalyze crashes. A concept of fractal theory called the Hurst exponent—a measure of the long-range dependence (LRD) of a time series—was used to understand the fluctuations in flow and speed of a motorway in Sydney, Australia. The spatial and temporal variation of the LRD for flow ( Hflow) and speed ( Hspeed) at several monitor sites is discussed. Furthermore, the effects of number of lanes on flow and speed predictability are explored. It was observed that the flow predictability of two-lane sections was significantly lower when compared with three-lane and four-lane sections. Conversely, the speed predictability of four-lane sections was considerably higher than that of two-lane and three-lane sections. Finally, traffic congestion was defined with regard to the LRD of speed, and its correlation with historical incident rates was measured. It was ascertained that monitor sites with a historically high proportion of large Hspeed were correlated with unsafe locations. This study could lead to many applications of fractal analysis on highways and urban traffic.

Empirical Evidence of Hurst Exponent Estimation Wavelet Based

2014 ◽  
Vol 687-691 ◽  
pp. 1668-1671
Author(s):  
Bin Luo ◽  
Tong Zhou Zhao ◽  
De Hua Li ◽  
Dun Bo Cai
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Wavelet Spectrum ◽  
Long Range Dependence ◽  
Range Analysis ◽  
Data Set ◽  
Massive Data Set ◽  
Rescaled Range ◽  
Rescaled Range Analysis ◽  
Original Time

In this paper, we study long-range dependence of hydrological records with high frequent and massive data set. For detecting breakpoints, we apply the Evolutionary Wavelet Spectrum (EWS) to provide a segmentation of the original time series. And rescaled range analysis (R/S) for estimating the Hurst exponent that describe the long-range dependence phenomenon are used. The results affirm that the hydrological records have long-range dependent (LRD) behaviors.

scholarly journals Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Francisco Gerardo Benavides-Bravo ◽  
F-Javier Almaguer ◽  
Roberto Soto-Villalobos ◽  
Víctor Tercero-Gómez ◽  
Javier Morales-Castillo
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Historical Data ◽  
Regional Frequency Analysis ◽  
Long Range Dependence ◽  
National Commission ◽  
Long Range Correlations ◽  
Rainfall Variations ◽  
Regional Frequency

An important topic in the study of the time series behavior and, in particular, meteorological time series is the long-range dependence. This paper explores the behavior of rainfall variations in different periods, using long-range correlations analysis. Semivariograms and Hurst exponent were applied to historical data in different pluviometric stations of the Río Bravo-San Juan watershed, at the hydrographic RH-24 Mexico region. The database was provided by the Water National Commission (CONAGUA). Using the semivariograms, the Hurst exponent was obtained and used as an input to perform a cluster analysis of rainfall stations. Groups of homogeneous samples that might be useful in a regional frequency analysis were obtained through the process.

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks (Extended and Renewed Version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Speed Computer

This paper presents an extension of the models used to generate fractal traffic flows in high-speed computer networks by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

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