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Ces notes sont consacrées aux inégalités et aux théorèmes limites classiques pour les suites de variables aléatoires absolument régulières ou fortement mélangeantes au sens de Rosenblatt. Le but poursuivi est de donner des outils techniques pour l'étude des processus faiblement dépendants aux statisticiens ou aux probabilistes travaillant sur ces processus.
Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.
This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.
Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, is a volume undertaken by the friends and colleagues of Sid Yakowitz in his honor. Fifty internationally known scholars have collectively contributed 30 papers on modeling uncertainty to this volume. Each of these papers was carefully reviewed and in the majority of cases the original submission was revised before being accepted for publication in the book. The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering, and economics departments, or just anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge. In sum, it is a book of considerable interest to a broad range of academic researchers and students of stochastic systems.