An Introduction To The Theory Of Large Deviations
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An Introduction To The Theory Of Large Deviations
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Author : Daniel W. Stroock
language : en
Publisher:
Release Date : 1984
An Introduction To The Theory Of Large Deviations written by Daniel W. Stroock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Large deviations categories.
An Introduction To The Theory Of Large Deviations
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Author : D.W. Stroock
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To The Theory Of Large Deviations written by D.W. Stroock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These notes are based on a course which I gave during the academic year 1983-84 at the University of Colorado. My intention was to provide both my audience as well as myself with an introduction to the theory of 1arie deviations • The organization of sections 1) through 3) owes something to chance and a great deal to the excellent set of notes written by R. Azencott for the course which he gave in 1978 at Saint-Flour (cf. Springer Lecture Notes in Mathematics 774). To be more precise: it is chance that I was around N. Y. U. at the time'when M. Schilder wrote his thesis. and so it may be considered chance that I chose to use his result as a jumping off point; with only minor variations. everything else in these sections is taken from Azencott. In particular. section 3) is little more than a rewrite of his exoposition of the Cramer theory via the ideas of Bahadur and Zabel. Furthermore. the brief treatment which I have given to the Ventsel-Freidlin theory in section 4) is again based on Azencott's ideas. All in all. the biggest difference between his and my exposition of these topics is the language in which we have written. However. another major difference must be mentioned: his bibliography is extensive and constitutes a fine introduction to the available literature. mine shares neither of these attributes. Starting with section 5).
Large Deviations
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Author : Frank Hollander
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Large Deviations written by Frank Hollander and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Large Deviations Techniques And Applications
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Author : Amir Dembo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Large Deviations Techniques And Applications written by Amir Dembo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Science categories.
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.
An Introduction To Markov Processes
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Author : Daniel W. Stroock
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-30
An Introduction To Markov Processes written by Daniel W. Stroock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-30 with Mathematics categories.
Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory Leads the reader to a rigorous understanding of basic theory
Large Deviations
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Author : Jean-Dominique Deuschel
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Large Deviations written by Jean-Dominique Deuschel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Large deviations categories.
This is the second printing of the book first published in 1988. The first four chapters of the 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
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Author : Frank den Hollander
language : en
Publisher:
Release Date : 2008
Large Deviations written by Frank den Hollander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
This book is an introduction to the theory and applications of large deviations, a branch of probability theory that describes the probability of rare events in terms of variational problems. By focusing the theory, in Part A of the book, on random sequences, the author succeeds in conveying the main ideas behind large deviations without a need for technicalities, thus providing a concise and accessible entry to this challenging and captivating subject. The selection of modern applications, described in Part B of the book, offers a good sample of what large deviation theory is able to achieve.
Large Deviations
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Author :
language : en
Publisher: Academic Press
Release Date : 1989-06-21
Large Deviations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-21 with Mathematics categories.
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).
A Course On Large Deviations With An Introduction To Gibbs Measures
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Author : Firas Rassoul-Agha
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-03-12
A Course On Large Deviations With An Introduction To Gibbs Measures written by Firas Rassoul-Agha and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
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.
Large Deviations For Stochastic Processes
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Author : Jin Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-03
Large Deviations For Stochastic Processes written by Jin Feng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-03 with Large deviations categories.
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.