Mathematical Statistics and Limit Theorems

Mathematical Statistics and Limit Theorems PDF

Author: Marc Hallin

Publisher: Springer

Published: 2015-04-07

Total Pages: 326

ISBN-13: 3319124420

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This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.

Modern Concepts and Theorems of Mathematical Statistics

Modern Concepts and Theorems of Mathematical Statistics PDF

Author: Edward B. Manoukian

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 168

ISBN-13: 1461248566

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With the rapid progress and development of mathematical statistical methods, it is becoming more and more important for the student, the in structor, and the researcher in this field to have at their disposal a quick, comprehensive, and compact reference source on a very wide range of the field of modern mathematical statistics. This book is an attempt to fulfill this need and is encyclopedic in nature. It is a useful reference for almost every learner involved with mathematical statistics at any level, and may supple ment any textbook on the subject. As the primary audience of this book, we have in mind the beginning busy graduate student who finds it difficult to master basic modern concepts by an examination of a limited number of existing textbooks. To make the book more accessible to a wide range of readers I have kept the mathematical language at a level suitable for those who have had only an introductory undergraduate course on probability and statistics, and basic courses in calculus and linear algebra. No sacrifice, how ever, is made to dispense with rigor. In stating theorems I have not always done so under the weakest possible conditions. This allows the reader to readily verify if such conditions are indeed satisfied in most applications given in modern graduate courses without being lost in extra unnecessary mathematical intricacies. The book is not a mere dictionary of mathematical statistical terms.

Limit Theorems in Probability, Statistics and Number Theory

Limit Theorems in Probability, Statistics and Number Theory PDF

Author: Peter Eichelsbacher

Publisher: Springer Science & Business Media

Published: 2013-04-23

Total Pages: 317

ISBN-13: 3642360688

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​Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.

Limit Theorems for Randomly Stopped Stochastic Processes

Limit Theorems for Randomly Stopped Stochastic Processes PDF

Author: Dmitriĭ Sergeevich Silʹvestrov

Publisher: Springer Science & Business Media

Published: 2004

Total Pages: 426

ISBN-13: 9781852337773

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Limit theorems for stochastic processes are an important part of probability theory and mathematical statistics and one model that has attracted the attention of many researchers working in the area is that of limit theorems for randomly stopped stochastic processes.This volume is the first to present a state-of-the-art overview of this field, with many of the results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast, and technically demanding, Russian literature in detail. A survey of the literature and an extended bibliography of works in the area are also provided.The coverage is thorough, streamlined and arranged according to difficulty for use as an upper-level text if required. It is an essential reference for theoretical and applied researchers in the fields of probability and statistics that will contribute to the continuing extensive studies in the area and remain relevant for years to come.

Stable Convergence and Stable Limit Theorems

Stable Convergence and Stable Limit Theorems PDF

Author: Erich Häusler

Publisher: Springer

Published: 2015-06-09

Total Pages: 228

ISBN-13: 331918329X

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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.

Limit Theorems for Associated Random Fields and Related Systems

Limit Theorems for Associated Random Fields and Related Systems PDF

Author: Aleksandr Vadimovich Bulinski?

Publisher: World Scientific

Published: 2007

Total Pages: 447

ISBN-13: 9812709401

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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.).

Limit Theorems of Probability Theory

Limit Theorems of Probability Theory PDF

Author: Yu.V. Prokhorov

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 280

ISBN-13: 3662041723

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A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.

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