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Stochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering.Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes.A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework. [Publisher]

Stochastic processes. --- Stochastic analysis. --- Stochastic differential equations. --- Dynamics. --- Processus stochastiques. --- Analyse stochastique. --- Équations différentielles stochastiques. --- Dynamique.

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Classical mechanics. Field theory --- Statistical physics --- Engineering sciences. Technology --- theoretische fysica --- systeemtheorie --- systeembeheer --- mechanica --- dynamica

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Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

Dynamics -- Congresses. --- Nonlinear theories -- Congresses. --- Stochastic processes -- Congresses. --- Dynamics --- Stochastic processes --- Nonlinear theories --- Civil & Environmental Engineering --- Physics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Atomic Physics --- Civil Engineering --- Physics. --- System theory. --- Mechanics. --- Statistical physics. --- Dynamical systems. --- Vibration. --- Dynamics. --- Nonlinear Dynamics. --- Vibration, Dynamical Systems, Control. --- Systems Theory, Control. --- Statistical Physics, Dynamical Systems and Complexity. --- Systems theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Classical Mechanics. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Classical mechanics --- Newtonian mechanics --- Quantum theory --- Cycles --- Mechanics --- Sound --- Statistical methods --- Systems, Theory of --- Systems science --- Science --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Philosophy