The overall objective of the book is to formulate the space-time dynamics of electromagnetic scattering processes from random media in terms of stochastic differential equations (SDEs), and to demonstrate the utility of this theoretical framework in model simulation and experimental data analysis. The author's key findings are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework in simulation and experimental data analysis. The physical models contain all correlation information and higher order statistics, which enables radar and laser scattering experiments to be interpreted. An emphasis is placed on the statistical character of the instantaneous fluctuations, as opposed to ensemble average properties. This leads to various means for detection, which have important consequences in radar signal processing and statistical optics. The book is also significant because it illustrates how ideas in mathematical finance can be applied to physics problems in which non-Gaussian noise processes play an essential role. This book represents a significant advance in this field, and should prove valuable to leading edge researchers and practitioners at the postgraduate level and above.
Stochastic Calculus | Heat Equation and Brownian Motion | Ito Calculus | Stochastic Differential Geometry | Examples of Stochastic Differential Equations | Dynamics of the Scattering Process | Diffusion Models of Scattering | Rayleigh Scattering | Population Dynamics | Dynamics of K-Scattering | Models of Weak Scattering | Scattering from General Populations | Simulation and Experiment | Simulation of K-Scattering | Experimental Tests | Non-Linear Dynamics of Sea Clutter | Observability of Scattering Cross-Section | Stability and Infinite Divisibility | Ito Versus Stratonovich Stochastic Integrals | Filtrations, Conditional Probability, and Markov Property | Girsanov's Theorem | Partition Function Solution to BDI Model | Summary of K-Scattering | Iterative Solution for Vector Processes | Open Problems | Suggested Further Reading