Stochastic Processes in Dynamics

 
9788301012984: Stochastic Processes in Dynamics

This book contains the theoretical foundations for the description of random phenomena in mechanics, with particular emphasis on dynamic systems. Before proceeding to basic ideas, the first chapter deals with certain fundamental problems of deterministic mechanics, such as: the differential equations of motion, the concept of configuration space, phase space, and the concept of stability. Then Chapter 2 presents the axiomatic foundations of the theory of stochastic processes and stochastic differential equations, emphasizing their analogy to mechanics. Following these fundamentals, the third chapter is devoted to a determination of probability density of functions of random variables. Also, it solves the problem of exceeding a boundary of domain by stochastic processes. The presentation is based on the sequential theory of stochastic processes. Chapter 4 presents the basic methods of stochastic dynamics of linear systems: correlation and spectral theory. The generalized spectral method in the theory of non-stationary processes is then considered. Finally, the applications of the correlation and spectral theory to systems with many degrees of freedom, as well as continuous systems are given. The fifth chapter presents the application of the kinetic Fokker-Planck-Kolmogorov equation to solving non-linear problems. Chapter 6 discusses fundamental concepts of stability in random systems. The extension of the direct Lyapounov method to investigating stability of stochastic systems is presented. The theoretical analysis is illustrated by a number of practical examples. The book contains an extensive listing of bibliography, East European particularly.

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Bogdan Skalmierski, Andrzej Tylikowski
Published by PWN + Martinus Nijhoff Publishers (1982)
ISBN 10: 8301012986 ISBN 13: 9788301012984
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Book Description PWN + Martinus Nijhoff Publishers, 1982. Book Condition: Very Good. Ships from the UK. Former Library book. Great condition for a used book! Minimal wear. Bookseller Inventory # GRP95607842

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Andrzej Tylikowski; Bogdan Skalmierski
Published by PWN + Martinus Nijhoff Publishers (1982)
ISBN 10: 8301012986 ISBN 13: 9788301012984
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Book Description PWN + Martinus Nijhoff Publishers, 1982. Hardcover. Book Condition: Near Fine. Cloth hardcover, translated from the Polish, vii + 149pp, references (pp.139-146) & index, NOT ex-library. --- Copy looks unread, interior is clean and bright throughout, with unmarked text and firm binding. Negligible light wear to very tips of some page corners. Gentle age-discolouration to edges of boards and a limited area of mid-front board. Dust jacket shows one very minor edge-nick, else untorn, with moderate creasing to edges, little scuffing, signs of regular shelfwear, a few scratches. --- This book contains the theoretical foundations for the description of random phenomena in mechanics, with particular emphasis on dynamic systems. Before proceeding to basic ideas, the first chapter deals with certain fundamental problems of deterministic mechanics, such as: the differential equations of motion, the concept of configuration space, phase space, and the concept of stability. Then Chapter 2 presents the axiomatic foundations of the theory of stochastic processes and stochastic differential equations, emphasizing their analogy to mechanics. Following these fundamentals, the third chapter is devoted to a determination of probability density of functions of random variables. Also, it solves the problem of exceeding a boundary of domain by stochastic processes. The presentation is based on the sequential theory of stochastic processes. Chapter 4 presents the basic methods of stochastic dynamics of linear systems: correlation and spectral theory. The generalized spectral method in the theory of non-stationary processes is then considered. Finally, the applications of the correlation and spectral theory to systems with many degrees of freedom, as well as continuous systems are given. The fifth chapter presents the application of the kinetic Fokker-Planck-Kolmogorov equation to solving non-linear problems. Chapter 6 discusses fundamental concepts of stability in random systems. The extension of the direct Lyapounov method to investigating stability of stochastic systems is presented. The theoretical analysis is illustrated by a number of practical examples. The book contains an extensive listing of bibliography, East European particularly. Bookseller Inventory # 002474

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