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...
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 co...
Time series and random ?elds are main topics in modern statistical techniques. They are essential for applications where randomness plays an important role. Indeed, physical constraints mean that serious modelling cannot be done - ing only independent sequences. This is a real problem because asymptotic properties are not always known in this case. Thepresentworkisdevotedtoprovidingaframeworkforthecommonlyused time series. In order to validate the main statistics, one needs rigorous limit theorems. In the ?eld of probability theory, asymptotic behavior of sums may or may not be analogous to...
Time series and random ?elds are main topics in modern statistical techniques. They are essential for applications where randomness plays an important...
The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written...
The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become...
This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.
This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex st...
Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important tool of analysis for random fields, Markov processes, central limit theorems as well as being a topic of current research interest in its own right. The aim of this monograph is to provide a study of applications of dependence in probability and statistics. It is divided in two parts, the first covering the definitions and probabilistic properties of mixing theory. The second part describes mixing properties of classical processes and random...
Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important to...
