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Author: Andrzej Lasota
Publisher: Cambridge University Press
ISBN: 9780521090964
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Andrzej Lasota
Publisher: Cambridge University Press
ISBN: 9780521090964
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Jiu Ding
Publisher: Springer Science & Business Media
ISBN: 3540853677
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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.
Author: Andrzej Lasota
Publisher: Springer Science & Business Media
ISBN: 146124286X
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Christos G. Cassandras
Publisher: CRC Press
ISBN: 1420008544
Category : Technology & Engineering
Languages : en
Pages : 301
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Book Description
Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.
Author: Annabelle McIver
Publisher: Springer Science & Business Media
ISBN: 038727006X
Category : Computers
Languages : en
Pages : 394
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Book Description
Illustrates by example the typical steps necessary in computer science to build a mathematical model of any programming paradigm . Presents results of a large and integrated body of research in the area of 'quantitative' program logics.
Author: Willi Semmler
Publisher: Routledge
ISBN: 1315288796
Category : Business & Economics
Languages : en
Pages : 275
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Book Description
As the 55th anniversary of the bank holiday of March 1933 approached, financial instability was a main topic in the financial press. Daily reports appeared of international debt crises, of the covert bankruptcy of deposit insurance, and of the near bankruptcy of one great financial institution after another. The great stock market crash of October 19 and 20, 1987, demonstrated that extreme instability can happen. It is generally asserted that the consequences of October 19th and 20th would have been disastrous if the Federal Reserve and Treasury interventions had not set things right. In 1933, financial markets in the United States and throughout the capitalist world collapsed. In the light of historical experience, the past 55 years are the anomaly. The papers collected in this volume come from various backgrounds and research paradigms. A common theme runs through these papers that makes the collection both interesting and important: The authors take seriously the obvious evidence that capitalist economies progress through time by lurching. Whether a particular study starts from household utility maximization or from the processes by which productive structures are reproduced and expanded, the authors are united in accepting the evidence that financial instability is a significant characteristic of modern capitalism.
Author: Aleksand Janicki
Publisher: CRC Press
ISBN: 1000445070
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.
Author: V.V. Kolbin
Publisher: Springer Science & Business Media
ISBN: 9789027707505
Category : Computers
Languages : en
Pages : 218
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Book Description
This book is devoted to the problems of stochastic (or probabilistic) programming. The author took as his basis the specialized lectures which he delivered to the graduates from the economic cybernetics department of Leningrad University beginning in 1967. Since 1971 the author has delivered a specialized course on Stochastic Programming to the gradu ates from the faculty of applied mathematics/management processes at Leningrad University. The present monograph consists of seven chapters. In Chapter I, which is of an introductory character, consideration is given to the problems of uncertainty and probability, used for modelling complicated systems. Fundamental indications for the classification of stochastic pro gramming problems are given. Chapter II is devoted to the analysis of various models of chance-constrained stochastic programming problems. Examples of technological and applied economic problems of management with chance-constraints are given. In Chapter III two-stage stochastic programming problems are investigated, various models are given, and these models are qualitatively analyzed. In the conclusion of the chapter consideration is given to: the transport problem with random data, the problem of the determination of production volume, and the problem of planning the flights of aircraft as two-stage stochastic programming problems. Multi-stage stochastic programming problems are investigated in Chapter IV. The dependencies between prior and posterior decision rules and decision distributions are given. Dual problems are investigated.
Author: Stephen Marshall
Publisher: Hindawi Publishing Corporation
ISBN: 9775945372
Category : Science
Languages : en
Pages : 375
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Book Description
Author: C.I. Byrnes
Publisher: Springer Science & Business Media
ISBN: 1475721358
Category : Science
Languages : en
Pages : 315
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Book Description
In its broadest sense, nonlinear synthesis involves in fact the synthesis of sometimes so phisticated or complex control strategies with the aim of prescribing, or at least influencing, the evolution of complex nonlinear systems. Nonlinear synthesis requires the development of methodologies for modeling complex systems, for the analysis of nonlinear models, and for the systematic design of control schemes or feedback laws which can achieve a wide variety of prescribed objectives. The modeling, analysis and control of complex systems in the face of uncertainty form on of the major components of the current research program in the Department of Systems and Decision Sciences (SDS) at the International Institute for Applied Systems Analysis (IIASA). In June 1989, a IIASA workshop on Nonlinear Synthesis, sponsored by SDS, was held in Sopron, Hungary. We are proud to present this volume as the proceedings of this workshop, a workshop attened by prominent researchers in nonlinear systems from both the East and the West. Since the promotion and encouragement of scientific cooperation between researchers in the East and in the West is one of the goals at IIASA, we feel the Sopron Conference on Nonlinear Synthesis was very successful. Moreover, we were especially pleased by the impressive new advances presented at the workshop which, in this volume, are now part of the conference record.
