Processes with Long-Range Correlations: Theory and Applications

R. J. Bhansali, P. S. Kokoszka (auth.), Prof. Govindan Rangarajan, Prof. Mingzhou Ding (eds.)3540401296, 9783540401292

Processes with long range correlations occur in a wide variety of fields ranging from physics and biology to economics and finance. This book, suitable for both graduate students and specialists, brings the reader up to date on this rapidly developing field. A distinguished group of experts have been brought together to provide a comprehensive and well-balanced account of basic notions and recent developments. The book is divided into two parts. The first part deals with theoretical developments in the area. The second part comprises chapters dealing primarily with three major areas of application: anomalous diffusion, economics and finance, and biology (especially neuroscience).

Table of contents :
Prediction of Long-Memory Time Series: A Tutorial Review….Pages 3-21
Fractional Brownian Motion and Fractional Gaussian Noise….Pages 22-33
Scaling and Wavelets: An Introductory Walk….Pages 34-60
Wavelet Estimation for the Hurst Parameter in Stable Processes….Pages 61-87
From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation….Pages 88-117
Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence….Pages 118-135
Supra-diffusion….Pages 139-147
Fractional diffusion Processes: Probability Distributions and Continuous Time Random Walk….Pages 148-166
First Passage Distributions for Long Memory Processes….Pages 167-180
Non-Gaussian Statistics and Anomalous diffusion in Porous Media….Pages 181-192
Directed Transport in AC-Driven Hamiltonian Systems….Pages 193-209
Patterns and Correlations in Economic Phenomena Uncovered Using Concepts of Statistical Physics….Pages 210-224
Semiparametric Modeling of Stochastic and Deterministic Trends and Fractional Stationarity….Pages 225-250
Interaction Models for Common Long-Range Dependence in Asset Prices Volatility….Pages 251-269
Long Memory and Economic Growth in the World Economy Since the 19th Century….Pages 270-285
Correlations and Memory in Neurodynamical Systems….Pages 286-308
Long Range Dependence in Human Sensorimotor Coordination….Pages 309-323
Scaling and Criticality in Large-Scale Neuronal Activity….Pages 324-338
Long-Range Dependence in Heartbeat Dynamics….Pages 339-372
Multifractals: From Modeling to Control of Broadband Network Traffic….Pages 373-392