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…mehr
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).
Theory.- Prediction of Long-Memory Time Series: A Tutorial Review.- Fractional Brownian Motion and Fractional Gaussian Noise.- Scaling and Wavelets: An Introductory Walk.- Wavelet Estimation for the Hurst Parameter in Stable Processes.- From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation.- Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence.- Applications.- Supra-diffusion.- Fractional diffusion Processes: Probability Distributions and Continuous Time Random Walk.- First Passage Distributions for Long Memory Processes.- Non-Gaussian Statistics and Anomalous diffusion in Porous Media.- Directed Transport in AC-Driven Hamiltonian Systems.- Patterns and Correlations in Economic Phenomena Uncovered Using Concepts of Statistical Physics.- Semiparametric Modeling of Stochastic and Deterministic Trends and Fractional Stationarity.- Interaction Models for Common Long-Range Dependence in Asset Prices Volatility.- Long Memory and Economic Growth in the World Economy Since the 19th Century.- Correlations and Memory in Neurodynamical Systems.- Long Range Dependence in Human Sensorimotor Coordination.- Scaling and Criticality in Large-Scale Neuronal Activity.- Long-Range Dependence in Heartbeat Dynamics.- Multifractals: From Modeling to Control of Broadband Network Traffic.
Theory.- Prediction of Long-Memory Time Series: A Tutorial Review.- Fractional Brownian Motion and Fractional Gaussian Noise.- Scaling and Wavelets: An Introductory Walk.- Wavelet Estimation for the Hurst Parameter in Stable Processes.- From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation.- Fractal Sums of Pulses and a Practical Challenge to the Distinction Between Local and Global Dependence.- Applications.- Supra-diffusion.- Fractional diffusion Processes: Probability Distributions and Continuous Time Random Walk.- First Passage Distributions for Long Memory Processes.- Non-Gaussian Statistics and Anomalous diffusion in Porous Media.- Directed Transport in AC-Driven Hamiltonian Systems.- Patterns and Correlations in Economic Phenomena Uncovered Using Concepts of Statistical Physics.- Semiparametric Modeling of Stochastic and Deterministic Trends and Fractional Stationarity.- Interaction Models for Common Long-Range Dependence in Asset Prices Volatility.- Long Memory and Economic Growth in the World Economy Since the 19th Century.- Correlations and Memory in Neurodynamical Systems.- Long Range Dependence in Human Sensorimotor Coordination.- Scaling and Criticality in Large-Scale Neuronal Activity.- Long-Range Dependence in Heartbeat Dynamics.- Multifractals: From Modeling to Control of Broadband Network Traffic.
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