Methods and Applications of White Noise Analysis in Interdisciplinary Sciences

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:

• Introduction
• White Noise Analysis: Some Basic Notions and Terminology
• Fluctuations with Memory
• Complex Systems
• Time Series Analysis
• Fluctuations without Memory
• Neurophysics
• Biopolymers
• White Noise Functional Integrals in Quantum Mechanics
• Quantum Particles with Boundary Conditions
• Relativistic Quantum Mechanics

Readership: Researchers in stochastic analysis, mathematical modeling and complex systems.
Key Features:

• White noise analysis is a relatively young mathematical research area. This volume will present and demonstrate how this new, powerful mathematical tool can be effectively utilized and applied to current problems in the interdisciplinary sciences
• It combines white noise analysis with the equally powerful Feynman path integral, thus allowing us to track the evolution even of systems with memory and strong correlations
• It is user-friendly