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Author : I. N. Sanov
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)
Download or read book On the Probability of Large Deviations of Random Variables written by I. N. Sanov and published by . This book was released on 1958 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Adam Shwartz
Publisher : CRC Press
ISBN 13 : 9780412063114
Total Pages : 576 pages
Book Rating : 4.0/5 (631 download)
Download or read book Large Deviations For Performance Analysis written by Adam Shwartz and published by CRC Press. This book was released on 1995-09-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (iid random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queueing models that might be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. Features: A transient analysis of the M/M/1 queue; a new analysis of an Aloha model using Markov modulated theory; new results for Erlang's model; new results for the AMS model; analysis of "serve the longer queue", "join the shorter queue" and other simple priority queues; and a simple analysis of the Flatto-Hahn-Wright model of processor-sharing.
Author : Victor H. Peña
Publisher : Springer Science & Business Media
ISBN 13 : 3540856366
Total Pages : 273 pages
Book Rating : 4.5/5 (48 download)
Download or read book Self-Normalized Processes written by Victor H. Peña and published by Springer Science & Business Media. This book was released on 2008-12-25 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.
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 : 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 : Firas Rassoul-Agha
Publisher : American Mathematical Soc.
ISBN 13 : 0821875787
Total Pages : 335 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Course on Large Deviations with an Introduction to Gibbs Measures written by Firas Rassoul-Agha and published by American Mathematical Soc.. This book was released on 2015-03-12 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the percolation approach. Beyond the large deviations of independent variables and Gibbs measures, later parts of the book treat large deviations of Markov chains, the Gärtner-Ellis theorem, and a large deviation theorem of Baxter and Jain that is then applied to a nonstationary process and a random walk in a dynamical random environment. The book has been used with students from mathematics, statistics, engineering, and the sciences and has been written for a broad audience with advanced technical training. Appendixes review basic material from analysis and probability theory and also prove some of the technical results used in the text.
Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
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 : Richard.S. Ellis
Publisher : Springer Science & Business Media
ISBN 13 : 1461385334
Total Pages : 372 pages
Book Rating : 4.4/5 (613 download)
Download or read book Entropy, Large Deviations, and Statistical Mechanics written by Richard.S. Ellis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of indepen dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure conver gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.
Author : Hugh L. Montgomery
Publisher : Cambridge University Press
ISBN 13 : 9780521849036
Total Pages : 574 pages
Book Rating : 4.8/5 (49 download)
Download or read book Multiplicative Number Theory I written by Hugh L. Montgomery and published by Cambridge University Press. This book was released on 2007 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Author : V.V. Petrov
Publisher : Springer Science & Business Media
ISBN 13 : 3642658091
Total Pages : 360 pages
Book Rating : 4.6/5 (426 download)
Download or read book Sums of Independent Random Variables written by V.V. Petrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity
Author : Sourav Chatterjee
Publisher : Springer
ISBN 13 : 3319658166
Total Pages : 175 pages
Book Rating : 4.3/5 (196 download)
Download or read book Large Deviations for Random Graphs written by Sourav Chatterjee and published by Springer. This book was released on 2017-08-31 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.
Author : Jin Feng
Publisher : American Mathematical Soc.
ISBN 13 : 0821841459
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)
Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2006 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are de
Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)
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.
Author : Yakov G. Sinai
Publisher : Springer Science & Business Media
ISBN 13 : 366202845X
Total Pages : 148 pages
Book Rating : 4.6/5 (62 download)
Download or read book Probability Theory written by Yakov G. Sinai and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics.
Author : Wassily Hoeffding
Publisher : Springer Science & Business Media
ISBN 13 : 1461208653
Total Pages : 653 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Collected Works of Wassily Hoeffding written by Wassily Hoeffding and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been a rare privilege to assemble this volume of Wassily Hoeffding's Collected Works. Wassily was, variously, a teacher, supervisor and colleague to us, and his work has had a profound influence on our own. Yet this would not be sufficient reason to publish his collected works. The additional and overwhelmingly compelling justification comes from the fun damental nature of his contributions to Statistics and Probability. Not only were his ideas original, and far-reaching in their implications; Wassily de veloped them so completely and elegantly in his papers that they are still cited as prime references up to half a century later. However, three of his earliest papers are cited rarely, if ever. These include material from his doctoral dissertation. They were written in German, and two of them were published in relatively obscure series. Rather than reprint the original articles, we have chosen to have them translated into English. These trans lations appear in this book, making Wassily's earliest research available to a wide audience for the first time. All other articles (including those of his contributions to Mathematical Reviews which go beyond a simple reporting of contents of articles) have been reproduced as they appeared, together with annotations and corrections made by Wassily on some private copies of his papers. Preceding these articles are three review papers which dis cuss the . impact of his work in some of the areas where he made major contributions.
Author : Yu.V. Prokhorov
Publisher : Springer Science & Business Media
ISBN 13 : 3662041723
Total Pages : 280 pages
Book Rating : 4.6/5 (62 download)
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
