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Stable Convergence And Stable Limit Theorems
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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 231 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.
Book Synopsis Stable Limit Theorems for Empirical Processes Under Conditional Neighborhood Dependence by : Ji Hyung Lee
Download or read book Stable Limit Theorems for Empirical Processes Under Conditional Neighborhood Dependence written by Ji Hyung Lee and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets are indexed by the same set endowed with a neighborhood system. When the set of random variables satisfies CND, any two non-adjacent sets of random variables are conditionally independent given sigma algebras having indices in one of the two sets' neighborhood. Random variables with CND include those with conditional dependency graphs and a class of Markov random fields with a global Markov property. The CND property is useful for modeling cross-sectional dependence governed by a complex, large network. This paper provides two main results. The first result is a stable central limit theorem for a sum of random variables with CND. The second result is a Donsker-type result of stable convergence of empirical processes indexed by a class of functions satisfying a certain bracketing entropy condition when the random variables satisfy CND. When there are high-degree vertices, they potentially hamper normal approximation by causing widespread dependence among the random variables. Thus we generalize the results by approximating the sum of random variables by the sum conditioned on high-degree vertices so that stable limit results continue to hold even when the maximum degree of the neighborhood system diverges to infinity as the size of the system grows.
Book Synopsis Limit Theorems For Associated Random Fields And Related Systems by : Alexander Bulinski
Download or read book Limit Theorems For Associated Random Fields And Related Systems written by Alexander Bulinski and published by World Scientific. This book was released on 2007-09-05 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.).
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.
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:
Book Synopsis Information Theory And The Central Limit Theorem by : Oliver T Johnson
Download or read book Information Theory And The Central Limit Theorem written by Oliver T 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.
Book Synopsis Functional Stable Limit Theorems by : David Ralph Beuerman
Download or read book Functional Stable Limit Theorems written by David Ralph Beuerman and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Book Synopsis Limit Theorems for Functionals of Sums that Converge to Fractional Stable Motions by : P. Jeganathan
Download or read book Limit Theorems for Functionals of Sums that Converge to Fractional Stable Motions written by P. Jeganathan and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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".
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
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 118 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.
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 485 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.
Book Synopsis Weak Convergence Theorems for Queues in Heavy Traffic by : Ward Whitt
Download or read book Weak Convergence Theorems for Queues in Heavy Traffic written by Ward Whitt and published by . This book was released on 1969 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
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).
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.
