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Field name	Details
Dewey Class	519.5
Title	Chaos: A Statistical Perspective ([EBook] /) / by Kung-Sik Chan, Howell Tong.
Author	Chan, Kung-Sik
Added Personal Name	Tong, Howell author.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York : : Imprint: Springer, , 2001.
Physical Details	XVI, 300 p. : online resource.
Series	Springer Series in Statistics 0172-7397
ISBN	9781475734645
Summary Note	It was none other than Henri Poincare who at the turn of the last century, recognised that initial-value sensitivity is a fundamental source of random ness. For statisticians working within the traditional statistical framework, the task of critically assimilating randomness generated by a purely de terministic system, often known as chaos, is an intellectual challenge. Like some other statisticians, we have taken up this challenge and our curiosity as reporters and participants has led us to investigate beyond the earlier discoveries in the field. Earlier statistical work in the area was mostly con cerned with the estimation of what is sometimes imprecisely called the fractal dimension. During the different stages of our writing, substantial portions of the book were used in lectures and seminars. These include the DMV (German Mathematical Society) Seminar Program, the inaugural session of lectures to the Crisis Points Project at the Peter Wall Institute of Advanced Stud ies, University of British Columbia and the graduate courses on Time Series Analysis at the University of Iowa, the University of Hong Kong, the Lon don School of Economics and Political Science, and the Chinese University of Hong Kong. We have therefore benefitted greatly from the comments and suggestions of these audiences as well as from colleagues and friends. We are grateful to them for their contributions. Our special thanks go to Colleen Cutler, Cees Diks, Barbel FinkensHidt, Cindy Greenwood, Masakazu Shi mada, Floris Takens and Qiwei Yao.:
Contents note	1 Introduction and Case Studies -- 2 Deterministic Chaos -- 3 Chaos and Stochastic Systems -- 4 Statistical Analysis I -- 5 Statistical Analysis II -- 6 Nonlinear Least-Square Prediction -- 7 Miscellaneous Topics -- Appendix A Deterministic Chaos -- A.1 Introduction -- A.2 Attracting Sets -- A.3 Another Look At the Logistic Maps -- A.4 Attractors -- A.5 Two Approaches to Studying Chaos -- A.6 Invariant and Ergodic Distributions -- A.7 Lyapunov Exponents -- A.8 Natural Measures -- A.9 Dimensions of an Attractor -- A.9.1 Box-Counting Dimension -- A.9.2 Correlation Dimension -- A.10 Map Reconstruction -- A. 11 Some Elements of Differentiable Manifolds -- A.12 Hyperbolic Sets -- A.13 Notes -- Appendix B Supplements to Chapter 3 -- B.1 Criteria for Ergodicity -- B.1.1 Notes -- B.2 Proofs of Two Theorems in §3.3.2 -- B.3 Shadowing and Hyperbolic Attractors -- Appendix C Data Sets and Software -- References -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-3464-5
Links to Related Works	Subject References: Chemometrics . Computational Intelligence . Dynamical Systems . Math. Applications in Chemistry . Probabilities . Probability theory and stochastic processes . Statistical Physics . Statistical Physics, Dynamical Systems and Complexity . Statistical Theory and Methods . Statistics . Authors: Chan, Kung-Sik . Tong, Howell . Corporate Authors: SpringerLink (Online service) . Series: Springer Series in Statistics . Classification: 519.5 .

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Chaos: A Statistical Perspective

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