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Author : Narasinga Rao Chaganty
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (95 download)
Download or read book Large Deviation Local Limit Theorems, with Applications written by Narasinga Rao Chaganty and published by . This book was released on 1982 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir Vinogradov
Publisher : CRC Press
ISBN 13 : 100094834X
Total Pages : 228 pages
Book Rating : 4.0/5 (9 download)
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 228 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
Author : Frank Hollander
Publisher : American Mathematical Soc.
ISBN 13 : 9780821844359
Total Pages : 164 pages
Book Rating : 4.8/5 (443 download)
Download or read book Large Deviations written by Frank Hollander and published by American Mathematical Soc.. This book was released on 2000 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Author :
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (227 download)
Download or read book Large Deviation Limit Theorems, with Applications written by and published by . This book was released on 1994 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research project we have established several landmark results in large deviation theory, invariant properties of common statistical tests, Bahadur efficiency computations and the study of standby redundant systems. These results have numerous applications to Statistical methodology, Monte carlo simulations, bootstrap methods and Bayesian statistics and in the study of reliability of systems.
Author : Amir Dembo
Publisher : Springer Science & Business Media
ISBN 13 : 3642033113
Total Pages : 409 pages
Book Rating : 4.6/5 (42 download)
Download or read book Large Deviations Techniques and Applications written by Amir Dembo and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.
Author : S. R. S. Varadhan
Publisher : SIAM
ISBN 13 : 0898711894
Total Pages : 74 pages
Book Rating : 4.8/5 (987 download)
Download or read book Large Deviations and Applications written by S. R. S. Varadhan and published by SIAM. This book was released on 1984-01-31 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Author : Jean-Dominique Deuschel
Publisher : American Mathematical Soc.
ISBN 13 : 082182757X
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)
Download or read book Large Deviations written by Jean-Dominique Deuschel and published by American Mathematical Soc.. This book was released on 2001 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second printing of the book first published in 1988. The first four chapters of the volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).
Author :
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (227 download)
Download or read book Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables with Applications written by and published by . This book was released on 1991 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research project we have obtained several limit theorems for arbitrary and dependent sequences of random variables. The limit theorems considered in this project fall into three categories namely, Large deviation local limit theorems, Strong large deviation theorems and Strong moderate deviation theorems. These three categories are dependent in the sense they all are subcategories of large deviation theory. The theory of large deviations and its many users are well described in the book by Ellis (1985) and the monograph by Varadhan (1984). This work generalized several classical limit theorems that were obtained in the literature for independent and identically distributed random variables. In the next three sections we outline briefly the technical details of the work done under this contract.
Author : Vladimir Vinogradov
Publisher : CRC Press
ISBN 13 : 1000941604
Total Pages : 226 pages
Book Rating : 4.0/5 (9 download)
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
Author :
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (227 download)
Download or read book Strong Large Deviation and Local Limit Theorems written by and published by . This book was released on 1986 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most large deviation results give asymptotic expressions to log P(Y sub n> or = X sub n) where the event (Y sub n> or = X sub n) is a large deviation event, that is, its probability goes to zero exponentially fast. The authors to such results for arbitrary random variables (Y sub n), that is, it obtains asymptotic expressions for P(Y sub n> or = X sub n) where (Y sub n> or = X sub n) is a large deviation event. These strong large deviation results are obtained for lattice valued and nonlattice valued random variables and require some conditions on their moment generating functions. A result that gives the average probability that Y sub n lies in an interval 2h/b sub n around the point Y sub n where h> 0, b sub n approaches limit of y*, is referred to as a local limit result for (Y sub n). This paper obtains local limit theorems for arbitrary random variables based on easily verifiable conditions on their characteristic functions. These local limit theorems play a major role in the proofs of the strong large deviation results of this paper. These results are illustrated with two typical applications.
Author : L. Saulis
Publisher : Springer Science & Business Media
ISBN 13 : 9401135304
Total Pages : 241 pages
Book Rating : 4.4/5 (11 download)
Download or read book Limit Theorems for Large Deviations written by L. Saulis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series
Author : A.D. Wentzell
Publisher : Springer Science & Business Media
ISBN 13 : 9400918526
Total Pages : 192 pages
Book Rating : 4.4/5 (9 download)
Download or read book Limit Theorems on Large Deviations for Markov Stochastic Processes written by A.D. Wentzell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum - the distribution of the value of a stochastic process at one (time) point - or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.
Author : Narasinga Rao Chaganty
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (227 download)
Download or read book Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Variables written by Narasinga Rao Chaganty and published by . This book was released on 1982 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results of W. Richter (Theory Prob. Appl. (1957) 2 206-219) on sums of independent, identically distributed random variables are generalized to arbitrary sequences of random variables Tn. Under simple conditions on the cumulant generating function of Tn, which imply that Tau n/n converges to o, it is shown, for arbitrary sequences (mn) converging to o, that kn(mn), the probability density function of Tn/n at mn, is asymptotic to an expression involving the large deviation rate of Tn/n. Analogous results for lattice random variables are also given. Applications of these results to statistics appearing in nonparametric inference are presented. (Author).
Author : Angelo Vulpiani
Publisher : Springer
ISBN 13 : 3642542514
Total Pages : 323 pages
Book Rating : 4.6/5 (425 download)
Download or read book Large Deviations in Physics written by Angelo Vulpiani and published by Springer. This book was released on 2014-05-16 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.
Author : Narasinga Rao Chaganty
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (246 download)
Download or read book Mathematical Sciences written by Narasinga Rao Chaganty and published by . This book was released on 1988 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank den Hollander
Publisher :
ISBN 13 : 9781470431419
Total Pages : 156 pages
Book Rating : 4.4/5 (314 download)
Download or read book Large Deviations written by Frank den Hollander and published by . This book was released on 2008 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve.
Author : Hans Fischer
Publisher : Springer Science & Business Media
ISBN 13 : 0387878572
Total Pages : 415 pages
Book Rating : 4.3/5 (878 download)
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
