Probabilistic Properties Of Deterministic Systems
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Probabilistic Properties Of Deterministic Systems
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Author : Andrzej Lasota
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
Probabilistic Properties Of Deterministic Systems written by Andrzej Lasota and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Statistical Properties Of Deterministic Systems
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Author : Jiu Ding
language : en
Publisher:
Release Date : 2009
Statistical Properties Of Deterministic Systems written by Jiu Ding and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Deterministic chaos categories.
Introduction To Probabilistic Automata
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Author : Azaria Paz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Introduction To Probabilistic Automata written by Azaria Paz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Introduction to Probabilistic Automata deals with stochastic sequential machines, Markov chains, events, languages, acceptors, and applications. The book describes mathematical models of stochastic sequential machines (SSMs), stochastic input-output relations, and their representation by SSMs. The text also investigates decision problems and minimization-of-states problems arising from concepts of equivalence and coverings for SSMs. The book presents the theory of nonhomogeneous Markov chains and systems in mathematical terms, particularly in relation to asymptotic behavior, composition (direct sum or product), and decomposition. "Word functions," induced by Markov chains and valued Markov systems, involve characterization, equivalence, and representability by an underlying Markov chain or system. The text also discusses the closure properties of probabilistic languages, events and their relation to regular events, particularly with reference to definite, quasidefinite, and exclusive events. Probabilistic automata theory has applications in information theory, control, learning theory, pattern recognition, and time sharing in computer programming. Programmers, computer engineers, computer instructors, and students of computer science will find the collection highly valuable.
Chaos Fractals And Noise
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Author : Andrzej Lasota
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Chaos Fractals And Noise written by Andrzej Lasota and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.
Statistical Properties Of Deterministic Systems
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Author : Jiu Ding
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-28
Statistical Properties Of Deterministic Systems written by Jiu Ding and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-28 with Mathematics categories.
Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
Stochastic Versus Deterministic Systems Of Iterative Processes
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Author : Gangaram S Ladde
language : en
Publisher:
Release Date : 2024-06-06
Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Mathematics categories.
State continuous dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend mode of convergence. Second, the basic probabilistic and statistical properties mean, variance, moments of qualitative/quantitative behaviour of solutions are directly described as concept of solution process or via probability distribution or density functions either. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focussed on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the problems outlined above and made slow progress in developing problems as a result. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Stochastic Versus Deterministic Systems Of Iterative Processes
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Author : Gangaram S Ladde
language : en
Publisher: World Scientific
Release Date : 2024-04-22
Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Mathematics categories.
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Deterministic Nonlinear Systems
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Author : Vadim S. Anishchenko
language : en
Publisher: Springer
Release Date : 2014-06-16
Deterministic Nonlinear Systems written by Vadim S. Anishchenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-16 with Science categories.
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Validation Of Stochastic Systems
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Author : Christel Baier
language : en
Publisher: Springer
Release Date : 2004-08-26
Validation Of Stochastic Systems written by Christel Baier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-26 with Mathematics categories.
This tutorial volume presents a coherent and well-balanced introduction to the validation of stochastic systems; it is based on a GI/Dagstuhl research seminar. Supervised by the seminar organizers and volume editors, established researchers in the area as well as graduate students put together a collection of articles competently covering all relevant issues in the area. The lectures are organized in topical sections on: modeling stochastic systems, model checking of stochastic systems, representing large state spaces, deductive verification of stochastic systems.
Probabilistic Systems Analysis
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Author : Arthur M. Breipohl
language : en
Publisher:
Release Date : 1970
Probabilistic Systems Analysis written by Arthur M. Breipohl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Elementary probability; Engineering applications of probability; Random variables; Expected values; Distribution of functions of Random variables; Applications of Random variables to systems problems; Distributions from data; Estimation; Engineering decisions; Introduction to Random processes; Systems and Random signals.