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Full Description
Analysis, modeling, and simulation for better understanding of diverse complex natural and social phenomena often require powerful tools and analytical methods. Tractable approaches, however, can be developed with mathematics beyond the common toolbox. This book presents the white noise stochastic calculus, originated by T Hida, as a novel and powerful tool in investigating physical and social systems. The calculus, when combined with Feynman's summation-over-all-histories, has opened new avenues for resolving cross-disciplinary problems. Applications to real-world complex phenomena are further enhanced by parametrizing non-Markovian evolution of a system with various types of memory functions. This book presents general methods and applications to problems encountered in complex systems, scaling in industry, neuroscience, polymer physics, biophysics, time series analysis, relativistic and nonrelativistic quantum systems.
Contents
White Noise Analysis: Basic Notion and Terminology; Fluctuations with and without Memory; Fractional Brownian Motion; Complex Systems; Scaling in Industry; Modeling Single Neuron Activities and Interneuronal Connections; Biopolymer Conformation; Hurst Exponent in Time Series Analysis; Quantum Mechanics with Topological Constraints and Boundaries; Relativistic Quantum Mechanics.
