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Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
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Mathematics Weak Dependence: With Examples and Applications (Lecture Notes in Statistics)
Posted on 2010-04-15
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Author: Sana Louhichi, Jos¨¦ Rafael Leon R., Gabriel Lang, Paul Doukhan, J¨¦r?me Dedecker, Cl¨¦mentine Prieur
Publisher: Springer (2007) Binding: Paperback, 322 pages pricer: $59.95 ISBN-10: 0387699511 editorialreviews This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength. The main existing tools for an asymptotic theory are developed under weak dependence. They apply the theory to nonparametric statistics, spectral analysis, econometrics, and resampling. The level of generality makes those techniques quite robust with respect to the model. The limit theorems are sometimes sharp and always simple to apply. The theory (with proofs) is developed and the authors propose to fix the notation for future applications. A large number of research papers deals with the present ideas; the authors as well as numerous other investigators participated actively in the development of this theory. Several applications are still needed to develop a method of analysis for (nonlinear) times series and they provide here a strong basis for such studies. checked checked no
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