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| Author | : Jong-Woo Jeon |
| Publisher | : |
| Total Pages | : 184 |
| Release | : 1979 |
| Genre | : Limit theorems (Probability theory) |
| ISBN | : |
| Author | : L. Saulis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 241 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401135304 |
"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 | : Amir Dembo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 409 |
| Release | : 2009-11-03 |
| Genre | : Science |
| ISBN | : 3642033113 |
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 | : Richard S. Ellis |
| Publisher | : Taylor & Francis |
| Total Pages | : 392 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9783540290599 |
From the reviews: "... Besides the fact that the author's treatment of large deviations is a nice contribution to the literature on the subject, his book has the virue that it provides a beautifully unified and mathematically appealing account of certain aspects of statistical mechanics. ... Furthermore, he does not make the mistake of assuming that his mathematical audience will be familiar with the physics and has done an admireable job of explaining the necessary physical background. Finally, it is clear that the author's book is the product of many painstaking hours of work; and the reviewer is confident that its readers will benefit from his efforts." D. Stroock in Mathematical Reviews 1985 "... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." S. Pogosian in Zentralblatt für Mathematik 1986
| Author | : S. R. S. Varadhan |
| Publisher | : SIAM |
| Total Pages | : 80 |
| Release | : 1984-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970241 |
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 | : Frank Hollander |
| Publisher | : Amer Mathematical Society |
| Total Pages | : 143 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780821819890 |
This volume offers an introduction to large deviations. It is divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence. The rate function is computed explicitly. The theory is explained without too much emphasis on technicalities. Also included is an outline of general definitions and theorems. The goal is to expose the unified theme that gives large deviation theoryits overall structure, which can be made to work in many concrete cases. The section on applications focuses on recent work in statistical physics and random media.This book contains 60 exercises (with solutions) that should elucidate the content and engage the reader. Prerequisites for the book are a strong background in probability and analysis and some knowledge of statistical physics. It would make an excellent textbook for a special topics course in large deviations.
| Author | : Vladimir Vinogradov |
| Publisher | : CRC Press |
| Total Pages | : 228 |
| Release | : 2023-06-14 |
| Genre | : Mathematics |
| ISBN | : 100094834X |
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 | : Boris Nahapetian |
| Publisher | : Springer |
| Total Pages | : 260 |
| Release | : 1991-08 |
| Genre | : Technology & Engineering |
| ISBN | : |
| Author | : Alexander Bulinski |
| Publisher | : World Scientific |
| Total Pages | : 447 |
| Release | : 2007-09-05 |
| Genre | : Mathematics |
| ISBN | : 9814474576 |
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.).
| Author | : R. R. Bahadur |
| Publisher | : SIAM |
| Total Pages | : 48 |
| Release | : 1971-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970630 |
A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff's theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.
