Philippe Soulier – författare

This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeperthan that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.

The purpose of this book is to give a detailed account of some recent devel- ments in the ?eld of probability and statistics for dependent data. It covers a wide range of topics from Markov chains theory, weak dependence, dynamical system to strong dependence and their applications. The title of this book has been somehow borrowed from the book ”Dependence in Probability and Statistics: a Survey of Recent Result” edited by Ernst Eberlein and Murad S. Taqqu, Birkh¨ auser (1986), which could serve as an excellent prerequisite for reading this book. We hope that the reader will ?nd it as useful and stimulating as the previous one. This book was planned during a conference, entitled “STATDEP2005: Statistics for dependent data”, organized by the Statistical Laboratory of the CREST (Research Center in Economy and Statistics), in Paris/Malako?, under the auspices of the French State Statistical Institute, INSEE. See http://www.crest.fr/pageperso/statdep2005/home.htm for some r- rospective informations. However this book is not a conference proceeding. This conference has witnessed the rapid growth of contributions on dep- dent data in the probabilistic and statistical literature and the need for a book covering recent developments scattered in various probability and s- tistical journals. To achieve such a goal, we have solicited some participants of the conferences as well as other specialists of the ?eld.

The purpose of this book is to give a detailed account of some recent devel- ments in the ?eld of probability and statistics for dependent data. It covers a wide range of topics from Markov chains theory, weak dependence, dynamical system to strong dependence and their applications. The title of this book has been somehow borrowed from the book ”Dependence in Probability and Statistics: a Survey of Recent Result” edited by Ernst Eberlein and Murad S. Taqqu, Birkh¨ auser (1986), which could serve as an excellent prerequisite for reading this book. We hope that the reader will ?nd it as useful and stimulating as the previous one. This book was planned during a conference, entitled “STATDEP2005: Statistics for dependent data”, organized by the Statistical Laboratory of the CREST (Research Center in Economy and Statistics), in Paris/Malako?, under the auspices of the French State Statistical Institute, INSEE. See http://www.crest.fr/pageperso/statdep2005/home.htm for some r- rospective informations. However this book is not a conference proceeding. This conference has witnessed the rapid growth of contributions on dep- dent data in the probabilistic and statistical literature and the need for a book covering recent developments scattered in various probability and s- tistical journals. To achieve such a goal, we have solicited some participants of the conferences as well as other specialists of the ?eld.

This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.