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Author: Jerzy Szulga
Publisher: CRC Press
ISBN: 9780412050916
Category : Mathematics
Languages : en
Pages : 610
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Book Description
Introduction to Random Chaos contains a wealth of information on this significant area, rooted in hypercontraction and harmonic analysis. Random chaos statistics extend the classical concept of empirical mean and variance. By focusing on the three models of Rademacher, Poisson, and Wiener chaos, this book shows how an iteration of a simple random principle leads to a nonlinear probability model- unifying seemingly separate types of chaos into a network of theorems, procedures, and applications. The concepts and techniques connect diverse areas of probability, algebra, and analysis and enhance numerous links between many fields of science. Introduction to Random Chaos serves researchers and graduate students in probability, analysis, statistics, physics, and applicable areas of science and technology.
Author: Jerzy Szulga
Publisher: CRC Press
ISBN: 9780412050916
Category : Mathematics
Languages : en
Pages : 610
Get Book Here
Book Description
Introduction to Random Chaos contains a wealth of information on this significant area, rooted in hypercontraction and harmonic analysis. Random chaos statistics extend the classical concept of empirical mean and variance. By focusing on the three models of Rademacher, Poisson, and Wiener chaos, this book shows how an iteration of a simple random principle leads to a nonlinear probability model- unifying seemingly separate types of chaos into a network of theorems, procedures, and applications. The concepts and techniques connect diverse areas of probability, algebra, and analysis and enhance numerous links between many fields of science. Introduction to Random Chaos serves researchers and graduate students in probability, analysis, statistics, physics, and applicable areas of science and technology.
Author: Jerzy Szulga
Publisher: Taylor & Francis
ISBN: 1351436643
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Introduction to Random Chaos contains a wealth of information on this significant area, rooted in hypercontraction and harmonic analysis. Random chaos statistics extend the classical concept of empirical mean and variance. By focusing on the three models of Rademacher, Poisson, and Wiener chaos, this book shows how an iteration of a simple random principle leads to a nonlinear probability model- unifying seemingly separate types of chaos into a network of theorems, procedures, and applications. The concepts and techniques connect diverse areas of probability, algebra, and analysis and enhance numerous links between many fields of science. Introduction to Random Chaos serves researchers and graduate students in probability, analysis, statistics, physics, and applicable areas of science and technology.
Author: Giovanni Peccati
Publisher: Springer Science & Business Media
ISBN: 8847016797
Category : Mathematics
Languages : en
Pages : 281
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Book Description
The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.
Author: Richard Kautz
Publisher: Oxford University Press
ISBN: 0199594570
Category : Mathematics
Languages : en
Pages : 384
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Book Description
One CD-ROM disc in pocket.
Author: Iwona Abrams
Publisher: Icon Books Ltd
ISBN: 1848317662
Category : Science
Languages : en
Pages : 300
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Book Description
If a butterfly flaps its wings in Brazil, does it cause a tornado in Texas? Chaos theory attempts to answer such baffling questions. The discovery of randomness in apparently predictable physical systems has evolved into a science that declares the universe to be far more unpredictable than we have ever imagined. Introducing Chaos explains how chaos makes its presence felt in events from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern maths and physics, and explores the relationship between chaos and complexity, the unifying theory which suggests that all complex systems evolve from a few simple rules. This is an accessible introduction to an astonishing and controversial theory.
Author: John Banks
Publisher: Cambridge University Press
ISBN: 9780521531047
Category : Mathematics
Languages : en
Pages : 310
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Book Description
When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.
Author: Flavio Lorenzelli
Publisher: CRC Press
ISBN: 0203214587
Category : Science
Languages : en
Pages : 236
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Book Description
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
Author: Leonard Smith
Publisher: Oxford University Press, USA
ISBN: 0192853783
Category : Mathematics
Languages : en
Pages : 201
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Book Description
Chaos exists in systems all around us. This introduction draws in philosophy, literature, and maths to explain Chaos Theory, showing the variety of its applications in the real world, from technology to global warming, politics, and even gambling on the stock market.
Author: J. R. Dorfman
Publisher: Cambridge University Press
ISBN: 0521655897
Category : Science
Languages : en
Pages : 303
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Book Description
Introduction to applications and techniques in non-equilibrium statistical mechanics of chaotic dynamics.
Author: Hans-Jürgen Stöckmann
Publisher: Cambridge University Press
ISBN: 0521592844
Category : Science
Languages : en
Pages : 386
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Book Description
Discusses quantum chaos, an important area of nonlinear science.
