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Strong Large Deviation And Local Limit Theorems
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Book Synopsis Strong Large Deviation and Local Limit Theorems by :
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.
Book Synopsis Multidimensional Strong Large Deviation Theorems by :
Download or read book Multidimensional Strong Large Deviation Theorems written by and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We obtain a strong large deviation result for arbitrary sequence of random vectors under simple and verifiable conditions on the moment generating functions. The key to this result is a local limit theorem for arbitrary sequences of random vectors which is also provided in this paper. The local limit theorem gives conditions on the characteristic functions of random vectors for their pseudo-density function to converge uniformly on bounded sets. We apply these results to the multivariate F-distribution. Large Deviations, Limit Theorems.
Book Synopsis Large Deviation Local Limit Theorems for Random Vectors by : Narasinga R. Chaganty
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).
Book Synopsis Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables with Applications by :
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.
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 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
Book Synopsis Limit Theorems for Large Deviations by : L. Saulis
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
Book Synopsis Large Deviation Local Limit Theorems for Ratio Statistics by : Narasinga Rao Chaganty
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.
Book Synopsis Large Deviation Local Limit Theorems, with Applications by : Narasinga Rao Chaganty
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:
Book Synopsis Large Deviation Local Limit Theorems for Arbitrary Sequences of Random Variables by : Narasinga Rao Chaganty
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).
Book Synopsis Universal Theory For Strong Limit Theorems Of Probability by : Andrei N Frolov
Download or read book Universal Theory For Strong Limit Theorems Of Probability written by Andrei N Frolov and published by World Scientific. This book was released on 2019-10-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book which the universal approach to strong laws of probability is discussed in. The universal theories are described for three important objects of probability theory: sums of independent random variables, processes with independent increments and renewal processes. Further generalizations are mentioned. Besides strong laws, large deviations are of independent interest. The case of infinite variations is considered as well. Readers can examine appropriate techniques and methods. Optimality of conditions is discussed.
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).
Book Synopsis Petrov's Local Limit Theorems for Large Deviations by : H. A. Cheong
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:
Book Synopsis Local Limit Theorems for Inhomogeneous Markov Chains by : Dmitry Dolgopyat
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.
Book Synopsis Large Deviations by : Frank Hollander
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.
Book Synopsis Large Deviations by : S. R. S. Varadhan
Download or read book Large Deviations written by S. R. S. Varadhan and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems for Associated Random Fields and Related Systems by : Aleksandr Vadimovich Bulinski?
Download or read book Limit Theorems for Associated Random Fields and Related Systems written by Aleksandr Vadimovich Bulinski? 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.).
