Stable Convergence And Stable Limit Theorems

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Stable Convergence and Stable Limit Theorems

Author : Erich Häusler
Publisher : Springer
ISBN 13 : 331918329X
Total Pages : 228 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Stable Convergence and Stable Limit Theorems by : Erich Häusler

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.

Covergence Theorems with a Stable Limit Law

Author : Gerd Christoph
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Covergence Theorems with a Stable Limit Law by : Gerd Christoph

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.

Limit Theorems for Associated Random Fields and Related Systems

Author :
Publisher :
ISBN 13 : 9814474576
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Limit Theorems for Associated Random Fields and Related Systems by :

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:

Some Limit Theorems for Stationary Sequences with Infinite Or Finite Variance

Author : Florin Avram
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Some Limit Theorems for Stationary Sequences with Infinite Or Finite Variance by : Florin Avram

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:

Probability

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Probability by : Rick Durrett

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.

Information Theory and the Central Limit Theorem

Author : Oliver Johnson
Publisher : World Scientific
ISBN 13 : 1783260610
Total Pages : 224 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Information Theory and the Central Limit Theorem by : Oliver Johnson

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

Limit Theorems for Associated Random Fields and Related Systems

Author : Aleksandr Vadimovich Bulinskii
Publisher : World Scientific
ISBN 13 : 981270941X
Total Pages : 447 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Limit Theorems for Associated Random Fields and Related Systems by : Aleksandr Vadimovich Bulinskii

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.

Limit Theorems for Unions of Random Closed Sets

Author : Ilya S. Molchanov
Publisher : Springer
ISBN 13 : 3540481117
Total Pages : 162 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Limit Theorems for Unions of Random Closed Sets by : Ilya S. Molchanov

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.

Probability Theory and Mathematical Statistics

Author : B. Grigelionis
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311231932X
Total Pages : 752 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis Probability Theory and Mathematical Statistics by : B. Grigelionis

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".

Refined Large Deviation Limit Theorems

Author : Vladimir Vinogradov
Publisher : CRC Press
ISBN 13 : 1000941604
Total Pages : 226 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Refined Large Deviation Limit Theorems by : Vladimir Vinogradov

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

Separating Information Maximum Likelihood Method for High-Frequency Financial Data

Author : Naoto Kunitomo
Publisher : Springer
ISBN 13 : 4431559302
Total Pages : 114 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Separating Information Maximum Likelihood Method for High-Frequency Financial Data by : Naoto Kunitomo

Download or read book Separating Information Maximum Likelihood Method for High-Frequency Financial Data written by Naoto Kunitomo and published by Springer. This book was released on 2018-06-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic explanation of the SIML (Separating Information Maximum Likelihood) method, a new approach to financial econometrics. Considerable interest has been given to the estimation problem of integrated volatility and covariance by using high-frequency financial data. Although several new statistical estimation procedures have been proposed, each method has some desirable properties along with some shortcomings that call for improvement. For estimating integrated volatility, covariance, and the related statistics by using high-frequency financial data, the SIML method has been developed by Kunitomo and Sato to deal with possible micro-market noises. The authors show that the SIML estimator has reasonable finite sample properties as well as asymptotic properties in the standard cases. It is also shown that the SIML estimator has robust properties in the sense that it is consistent and asymptotically normal in the stable convergence sense when there are micro-market noises, micro-market (non-linear) adjustments, and round-off errors with the underlying (continuous time) stochastic process. Simulation results are reported in a systematic way as are some applications of the SIML method to the Nikkei-225 index, derived from the major stock index in Japan and the Japanese financial sector.

Séminaire de Probabilités XL

Author : Catherine Donati-Martin
Publisher : Springer
ISBN 13 : 3540711899
Total Pages : 489 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Séminaire de Probabilités XL by : Catherine Donati-Martin

Download or read book Séminaire de Probabilités XL written by Catherine Donati-Martin and published by Springer. This book was released on 2007-07-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who could have predicted that the S ́ eminaire de Probabilit ́ es would reach the age of 40? This long life is ?rst due to the vitality of the French probabil- tic school, for which the S ́ eminaire remains one of the most speci?c media of exchange. Another factor is the amount of enthusiasm, energy and time invested year after year by the R ́ edacteurs: Michel Ledoux dedicated himself tothistaskuptoVolumeXXXVIII,andMarcYormadehisnameinseparable from the S ́ eminaire by devoting himself to it during a quarter of a century. Browsing among the past volumes can only give a faint glimpse of how much is owed to them; keeping up with the standard they have set is a challenge to the new R ́ edaction. In a changing world where the status of paper and ink is questioned and where, alas, pressure for publishing is increasing, in particular among young mathematicians, we shall try and keep the same direction. Although most contributions are anonymously refereed, the S ́ eminaire is not a mathema- cal journal; our ?rst criterion is not mathematical depth, but usefulness to the French and international probabilistic community. We do not insist that everything published in these volumes should have reached its ?nal form or be original, and acceptance–rejection may not be decided on purely scienti?c grounds.

Univariate Stable Distributions

Author : John P. Nolan
Publisher : Springer Nature
ISBN 13 : 3030529150
Total Pages : 342 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Univariate Stable Distributions by : John P. Nolan

Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.

Young Measures on Topological Spaces

Author : Charles Castaing
Publisher : Springer Science & Business Media
ISBN 13 : 1402019637
Total Pages : 327 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Young Measures on Topological Spaces by : Charles Castaing

Download or read book Young Measures on Topological Spaces written by Charles Castaing and published by Springer Science & Business Media. This book was released on 2004-07-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Young measures are now a widely used tool in the Calculus of Variations, in Control Theory, in Probability Theory and other fields. They are known under different names such as "relaxed controls", "fuzzy random variables" and many other names. This monograph provides a unified presentation of the theory, along with new results and applications in various fields. It can serve as a reference on the subject. Young measures are presented in a general setting which includes finite and for the first time infinite dimensional spaces: the fields of applications of Young measures (Control Theory, Calculus of Variations, Probability Theory...) are often concerned with problems in infinite dimensional settings. The theory of Young measures is now well understood in a finite dimensional setting, but open problems remain in the infinite dimensional case. We provide several new results in the general frame, which are new even in the finite dimensional setting, such as characterizations of convergence in measure of Young measures (Chapter 3) and compactness criteria (Chapter 4).These results are established under a different form (and with fewer details and developments) in recent papers by the same authors. We also provide new applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).

Martingale Limit Theory and Its Application

Author : P. Hall
Publisher : Academic Press
ISBN 13 : 1483263223
Total Pages : 321 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Martingale Limit Theory and Its Application by : P. Hall

Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Stability Problems for Stochastic Models

Author : Vladimir V. Kalashnikov
Publisher : Springer
ISBN 13 : 3540473947
Total Pages : 230 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Stability Problems for Stochastic Models by : Vladimir V. Kalashnikov

Download or read book Stability Problems for Stochastic Models written by Vladimir V. Kalashnikov and published by Springer. This book was released on 2006-11-14 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extraction of Quantifiable Information from Complex Systems

Author : Stephan Dahlke
Publisher : Springer
ISBN 13 : 3319081594
Total Pages : 446 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Extraction of Quantifiable Information from Complex Systems by : Stephan Dahlke

Download or read book Extraction of Quantifiable Information from Complex Systems written by Stephan Dahlke and published by Springer. This book was released on 2014-11-13 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.