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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 : 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 :
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 : 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 : 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 : 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 : 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 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 : Narasinga Rao Chaganty
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.:/5 (227 download)
Download or read book Large Deviation Local Limit Theorems for Ratio Statistics written by Narasinga Rao Chaganty and published by . This book was released on 1987 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document discusses an arbitrary sequence of non-lattice random variables and another sequence of positive random variables. Assume that the sequences are independent. This paper obtains asymptotic expression for the density function of the ratio statistic R sub n = T sub n/S sub n based on simple conditions on the moment generating functions of T sub n and S sub n. When S sub n = n, our main result reduces to that of Chaganty and Sethuraman. We also obtain analogous results when T sub n and S sub n are both lattice random variables. We call our theorems large deviation local limit theorems for R sub n, since the conditions of our theorems imply that R sub n approaches limit of c in probability for some constant c. We present some examples to illustrate our theorems.
Author : S. R. S. Varadhan
Publisher : SIAM
ISBN 13 : 9781611970241
Total Pages : 80 pages
Book Rating : 4.9/5 (72 download)
Download or read book Large Deviations and Applications written by S. R. S. Varadhan and published by SIAM. This book was released on 1984-01-01 with total page 80 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 : Narasinga R. Chaganty
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (227 download)
Download or read book Large Deviation Local Limit Theorems for Random Vectors written by Narasinga R. Chaganty and published by . This book was released on 1986 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a survey of large deviation local limit theorems for random vectors. The authors then establish a more extensive large deviation local limit theorem that requires somewhat weaker conditions even in the special cases proved earlier. (Author).
Author : L. Saulis
Publisher : Springer Science & Business Media
ISBN 13 : 9780792314752
Total Pages : 252 pages
Book Rating : 4.3/5 (147 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 1991-10-31 with total page 252 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 : Dmitry Dolgopyat
Publisher : Springer Nature
ISBN 13 : 3031326016
Total Pages : 348 pages
Book Rating : 4.0/5 (313 download)
Download or read book Local Limit Theorems for Inhomogeneous Markov Chains written by Dmitry Dolgopyat and published by Springer Nature. This book was released on 2023-07-31 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
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 : H. A. Cheong
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (968 download)
Download or read book Petrov's Local Limit Theorems for Large Deviations written by H. A. Cheong and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jong-Woo Jeon
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.:/5 (63 download)
Download or read book Central Limit Theorems in the Regions of Large Deviations with Applications to Statistical Mechanics written by Jong-Woo Jeon and published by . This book was released on 1979 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 0080874576
Total Pages : 329 pages
Book Rating : 4.0/5 (88 download)
Download or read book Large Deviations written by and published by Academic Press. This book was released on 1989-06-21 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this 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).
