Large Deviations

Mathematics
Large Deviations PDF Author:
Publisher: Academic Press
ISBN: 9780080874579
Category : Mathematics
Languages : en
Pages : 306

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Book Description
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).

Large Deviations

Large Deviations PDF Author:
Publisher: Academic Press
ISBN: 9780080874579
Category : Mathematics
Languages : en
Pages : 306

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Book Description
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).

Admiralty Manual for Ascertaining and Applying the Deviations of the Compass Caused by the Iron in a Ship

Admiralty Manual for Ascertaining and Applying the Deviations of the Compass Caused by the Iron in a Ship PDF Author: Frederick John Evans
Publisher:
ISBN:
Category : Compass
Languages : en
Pages : 202

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Entropy, Large Deviations, and Statistical Mechanics

Entropy, Large Deviations, and Statistical Mechanics PDF Author: Richard S. Ellis
Publisher: Springer
ISBN: 3540290605
Category : Mathematics
Languages : en
Pages : 367

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Book Description
From the reviews: "... 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

Large Deviations

Large Deviations PDF Author: Frank den Hollander
Publisher: American Mathematical Soc.
ISBN: 0821871722
Category : Mathematics
Languages : en
Pages : 146

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Limit Theorems for Large Deviations

Limit Theorems for Large Deviations PDF Author: L. Saulis
Publisher: Springer Science & Business Media
ISBN: 9401135304
Category : Mathematics
Languages : en
Pages : 232

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Book Description
"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

Large Deviations

Large Deviations PDF Author: S. R. S. Varadhan
Publisher: American Mathematical Soc.
ISBN: 082184086X
Category : Large deviations
Languages : en
Pages : 104

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Book Description
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.

The Mathematical Theory of the Deviations of the Compass

The Mathematical Theory of the Deviations of the Compass PDF Author: John Adams Howell
Publisher:
ISBN:
Category : Compass
Languages : en
Pages : 150

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Large Deviations Techniques and Applications

Large Deviations Techniques and Applications PDF Author: Amir Dembo
Publisher: Springer Science & Business Media
ISBN: 3642033113
Category : Science
Languages : en
Pages : 396

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Book Description
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.

Large Deviations for Discrete-Time Processes with Averaging

Large Deviations for Discrete-Time Processes with Averaging PDF Author: O. V. Goulinskï
Publisher: VSP
ISBN: 9789067641487
Category : Mathematics
Languages : en
Pages : 200

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Book Description
This book is mainly based on the Cramir--Chernoff renowned theorem, which deals with the 'rough' logarithmic asymptotics of the distribution of sums of independent, identically distributed random variables. The authors approach primarily the extensions of this theory to dependent, and in particular, nonmarkovian cases on function spaces. Recurrent algorithms of identification and adaptive control form the main examples behind the large deviation problems in this volume. The first part of the book exploits some ideas and concepts of the martingale approach, especially the concept of the stochastic exponential. The second part of the book covers Freindlin's approach, based on the Frobenius-type theorems for positive operators, which prove to be effective for the cases in consideration.

Large Deviations for Stochastic Processes

Large Deviations for Stochastic Processes PDF Author: Jin Feng
Publisher: American Mathematical Soc.
ISBN: 1470418703
Category :
Languages : en
Pages : 410

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Book Description
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 derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.