Theory and Applications of LongRange DependencePaul Doukhan, George Oppenheim, Murad Taqqu The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even nonspecialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of longrange dependence in the data. This important topic of longrange dependence is the focus of this unique work, written by a number of specialists on the subject.
The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic longrange dependence, parametric, semiparametric, and nonparametric estimation, longmemory stochastic volatility models, robust estimation, and prediction for longrange dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques."
Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic longrange dependence, parametric, semiparametric, and nonparametric estimation, longmemory stochastic volatility models, robust estimation, prediction for longrange dependence sequences. The reader is referred to more detailed proofs if already found in the literature.
The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a stateofthe art reference or graduate seminar text.

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Contents
Historical Comments Related to Fractional Brownian Motion  39 
Models Inequalities and Limit Theorems for Stationary Sequences  43 
Limit Theorems under Seasonal LongMemory  101 
Diagram Formula with Illustrations  111 
UStatistics Multinomial Formula and Approximations of Multiple ItoWiener Integrals  129 
A Decomposition for Generalized UStatistics of LongMemory Linear Processes  143 
Limit Theorems for Infinite Variance Sequences  157 
Fractional Calculus and Its Connections to Fractional Brownian Motion  165 
Applications  369 
Applications  371 
LongRange Dependence and Data Network Traffic  373 
Large Deviations of Queues with LongRange Dependent Input  409 
The LongRange Dependence Paradigm for Macroeconomics and Finance  417 
Thomas Mikosch  439 
LongRange Dependence in Hydrology  461 
Wavelet Based Estimation of Local Kolmogorov Turbulence  473 
Stochastic Integration with Respect to Fractional Brownian Motion  203 
Statistics  227 
Parametric Estimation Under LongRange Dependence  229 
Semiparametric Spectral Estimation for Fractional Processes  251 
Nonparametric Estimation for LongRange Dependent Sequences  303 
Estimation of Long Memory in Volatility  313 
Detection and Estimation of Changes in Regime  325 
Robust Estimators in Regression Models with Long Memory Errors  339 
Prediction of LongMemory Time Series  355 
Limit Theorems for the Burgers Equation Initialized by Data with LongRange Dependence  507 
Methodology  525 
SelfSimilarity and LongRange Dependence through the Wavelet Lens  527 
A Survey  557 
A Survey  579 
Multifractal Processes  625 
List of Authors  717 