Stable Convergence And Stable Limit Theorems
DOWNLOAD
Download Stable Convergence And Stable Limit Theorems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Stable Convergence And Stable Limit Theorems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Stable Convergence And Stable Limit Theorems
DOWNLOAD
Author : Erich Häusler
language : en
Publisher: Springer
Release Date : 2015-06-09
Stable Convergence And Stable Limit Theorems written by Erich Häusler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-09 with Mathematics categories.
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level with a solid knowledge of measure theoretic probability.
Covergence Theorems With A Stable Limit Law
DOWNLOAD
Author : Gerd Christoph
language : en
Publisher: Wiley-VCH
Release Date : 1992-12-15
Covergence Theorems With A Stable Limit Law written by Gerd Christoph and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-15 with Mathematics categories.
The book deals with Berry-Esseen-type inequalities, asymptotic expansions, non-uniform estimates, U-statistics, and the density problem.
Some Limit Theorems For Stationary Sequences With Infinite Or Finite Variance
DOWNLOAD
Author : Florin Avram
language : en
Publisher:
Release Date : 1986
Some Limit Theorems For Stationary Sequences With Infinite Or Finite Variance written by Florin Avram and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Central limit theorem categories.
Limit Theorems For Associated Random Fields And Related Systems
DOWNLOAD
Author :
language : en
Publisher:
Release Date :
Limit Theorems For Associated Random Fields And Related Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Limit Theorems For Unions Of Random Closed Sets
DOWNLOAD
Author : Ilya S. Molchanov
language : en
Publisher: Springer
Release Date : 2006-11-15
Limit Theorems For Unions Of Random Closed Sets written by Ilya S. Molchanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed.
Information Theory And The Central Limit Theorem
DOWNLOAD
Author : Oliver Johnson
language : en
Publisher: World Scientific
Release Date : 2004-07-14
Information Theory And The Central Limit Theorem written by Oliver Johnson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-14 with Mathematics categories.
This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. Contents:Introduction to Information TheoryConvergence in Relative EntropyNon-Identical Variables and Random VectorsDependent Random VariablesConvergence to Stable LawsConvergence on Compact GroupsConvergence to Poisson DistributionFree Random Variables Readership: Graduate students, academics and researchers in probability and statistics. Key Features:Presents surprising, interesting connections between two apparently separate areas of mathematicsWritten by one of the researchers who discovered these connectionsOffers a new way of looking at familiar resultsKeywords:Information Theory;Entropy;Fisher Information;Central Limit Theorem;Probability;Statistics;Convergence of Random VariablesReviews:“This book provides a well-written and motivating introduction to information theory and a detailed description of the current research regarding the connections between central limit theorems and information theory. It is an important reference for many graduate students and researchers in this domain.”Mathematical Reviews
Limit Theorems For Associated Random Fields And Related Systems
DOWNLOAD
Author : Aleksandr Vadimovich Bulinskii
language : en
Publisher: World Scientific
Release Date : 2007
Limit Theorems For Associated Random Fields And Related Systems written by Aleksandr Vadimovich Bulinskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications. There are 434 items in the bibliography. The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.). Contents: Random Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.
Weak Convergence Theorems For Queues In Heavy Traffic
DOWNLOAD
Author : Ward Whitt
language : en
Publisher:
Release Date : 1969
Weak Convergence Theorems For Queues In Heavy Traffic written by Ward Whitt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Queuing theory categories.
Limit theorems are proved for unstable queueing systems. The GI/G/1 queue is the primary concern, but the theorems apply to more general systems in which the various independence assumptions are relaxed. Bulk queues, queues with several servers (GI/M/s), queues with a finite waiting room, and dams are also discussed. (Author).
Stopped Random Walks
DOWNLOAD
Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Stopped Random Walks written by Allan Gut and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Examples are sequential analysis, queuing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of contours. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimenstional random walks, and to how these results are useful in various applications. This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus "noise."
Limit Theorems For Some Long Range Random Walks On Torsion Free Nilpotent Groups
DOWNLOAD
Author : Zhen-Qing Chen
language : en
Publisher: Springer Nature
Release Date : 2023-11-25
Limit Theorems For Some Long Range Random Walks On Torsion Free Nilpotent Groups written by Zhen-Qing Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-25 with Mathematics categories.
This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.