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Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments. This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients. The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time. The book is addressed to students and researchers in applied mathematics that are interested in understanding how tools from stochastic analysis can be used to study some intriguing phenomena in wave propagation in random media. Parts of the book can be used for courses in which random media and related homogenization, averaging, and diffusion approximation methods are involved.

Time reversal. --- Random measures. --- Waves. --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Measures, Random --- Orthogonal random measures --- Measure theory --- Stochastic processes --- Reversal, Time --- Nuclear physics --- Quantum theory --- Space and time --- Mechanics. --- Mathematics. --- Distribution (Probability theory. --- Differential equations, partial. --- Classical Mechanics. --- Applications of Mathematics. --- Probability Theory and Stochastic Processes. --- Complex Systems. --- Partial Differential Equations. --- Fluid- and Aerodynamics. --- Partial differential equations --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Statistical physics. --- Dynamical systems. --- Partial differential equations. --- Fluids. --- Engineering --- Engineering analysis --- Mathematical analysis --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Mathematical statistics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Statistical methods

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Scattering (Physics) --- Space and time --- Time reversal --- Wave-motion, Theory of --- 519.21 --- 519.22 --- Reversal, Time --- Nuclear physics --- Quantum theory --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Undulatory theory --- Mechanics --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- Statistical theory. Statistical models. Mathematical statistics in general --- 519.21 Probability theory. Stochastic processes --- Probability theory. Stochastic processes --- Scattering --- Scattering (physics) --- Wave-motion, theory of

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Money market. Capital market --- Stochastic processes --- Derivative securities --- Financial institutions --- Instruments dérivés (Finances) --- Institutions financières --- 368.01 --- Financial intermediaries --- Lending institutions --- Associations, institutions, etc. --- Derivative financial instruments --- Derivative financial products --- Derivative instruments --- Derivatives (Finance) --- Financial derivatives --- Securities --- Structured notes (Securities) --- Derivative securities. --- Financial institutions. --- Instruments dérivés (Finances) --- Institutions financières

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The main theme of this volume is credit risk and credit derivatives. Recent developments in financial markets show that appropriate modeling and quantification of credit risk is fundamental in the context of modern complex structured financial products. The reader will find several points of view on credit risk when looked at from the perspective of Econometrics and Financial Mathematics. The volume consists of eleven contributions by both practitioners and theoreticians with expertise in financial markets, in general, and econometrics and mathematical finance in particular. The challenge of modeling defaults and their correlations is addressed, and new results on copula, reduced form and structural models, and the top-down approach are presented. After the so-called subprime crisis that hit global markets in the summer of 2007, the volume is very timely and will be useful to researchers in the area of credit risk.

Credit -- Mathematical models. --- Credit derivatives -- Mathematical models. --- Risk management -- Mathematical models. --- Credit derivatives --- Credit --- Econometrics --- Risk management --- Insurance --- Management --- Borrowing --- Finance --- Money --- Loans --- Derivative securities --- Mathematical models --- Quantitative methods (economics) --- International financial management --- Business & Economics --- Econometrics. --- Forecasting. --- Economics, Mathematical --- Statistics

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Wave propagation in random media is an interdisciplinary field that has emerged from the need in physics and engineering to model and analyze wave energy transport in complex environments. This book gives a systematic and self-contained presentation of wave propagation in randomly layered media using the asymptotic theory of ordinary differential equations with random coefficients. The first half of the book gives a detailed treatment of wave reflection and transmission in one-dimensional random media, after introducing gradually the tools from partial differential equations and probability theory that are needed for the analysis. The second half of the book presents wave propagation in three-dimensional randomly layered media along with several applications, primarily involving time reversal. Many new results are presented here for the first time. The book is addressed to students and researchers in applied mathematics that are interested in understanding how tools from stochastic analysis can be used to study some intriguing phenomena in wave propagation in random media. Parts of the book can be used for courses in which random media and related homogenization, averaging, and diffusion approximation methods are involved.

Partial differential equations --- Operational research. Game theory --- Mathematics --- Gases handling. Fluids handling --- Engineering sciences. Technology --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde --- stochastische analyse --- ingenieurswetenschappen --- kansrekening --- vloeistoffen