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The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up.

Vector-valued measures. --- Random measures. --- Measures, Random --- Orthogonal random measures --- Measure theory --- Stochastic processes --- Measures, Vector-valued --- Radon measures

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Animal physiology. Animal biophysics --- Branching processes --- Random measures --- Stochastic analysis --- Analyse stochastique --- Mesures aléatoires --- Processus ramifiés --- 2ram --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Measures, Random --- Orthogonal random measures --- Measure theory --- Processes, Branching --- Analyse stochastique. --- Mesures aléatoires.

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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