Stable Convergence And Stable Limit Theorems

Author : Erich Häusler
Publisher : Springer
ISBN 13 : 331918329X
Total Pages : 228 pages
Book Rating : 4.99/5 ( download)

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Download or read book Stable Convergence and Stable Limit Theorems written by Erich Häusler and published by Springer. This book was released on 2015-06-09 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Gerd Christoph
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.31/5 ( download)

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Download or read book Covergence Theorems with a Stable Limit Law written by Gerd Christoph and published by Wiley-VCH. This book was released on 1992-12-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with Berry-Esseen-type inequalities, asymptotic expansions, non-uniform estimates, U-statistics, and the density problem.

Author :
Publisher :
ISBN 13 : 9814474576
Total Pages : pages
Book Rating : 4.73/5 ( download)

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Download or read book Limit Theorems for Associated Random Fields and Related Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Florin Avram
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.81/5 ( download)

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Download or read book Some Limit Theorems for Stationary Sequences with Infinite Or Finite Variance written by Florin Avram and published by . This book was released on 1986 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.36/5 ( download)

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Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Author : Oliver Johnson
Publisher : World Scientific
ISBN 13 : 1783260610
Total Pages : 224 pages
Book Rating : 4.14/5 ( download)

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Download or read book Information Theory and the Central Limit Theorem written by Oliver Johnson and published by World Scientific. This book was released on 2004-07-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Aleksandr Vadimovich Bulinskii
Publisher : World Scientific
ISBN 13 : 981270941X
Total Pages : 447 pages
Book Rating : 4.17/5 ( download)

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Download or read book Limit Theorems for Associated Random Fields and Related Systems written by Aleksandr Vadimovich Bulinskii and published by World Scientific. This book was released on 2007 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ilya S. Molchanov
Publisher : Springer
ISBN 13 : 3540481117
Total Pages : 162 pages
Book Rating : 4.19/5 ( download)

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Download or read book Limit Theorems for Unions of Random Closed Sets written by Ilya S. Molchanov and published by Springer. This book was released on 2006-11-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : B. Grigelionis
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311231932X
Total Pages : 752 pages
Book Rating : 4.21/5 ( download)

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Download or read book Probability Theory and Mathematical Statistics written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probability Theory and Mathematical Statistics".

Author : Vladimir Vinogradov
Publisher : CRC Press
ISBN 13 : 1000941604
Total Pages : 226 pages
Book Rating : 4.09/5 ( download)

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Download or read book Refined Large Deviation Limit Theorems written by Vladimir Vinogradov and published by CRC Press. This book was released on 2023-06-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramér's condition on the finiteness of exponential moments may not be satisfied