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Large Deviations Techniques and Applications

Large Deviations Techniques and Applications PDF Author: Amir Dembo
Publisher: Springer
ISBN: 9783642033100
Category : Science
Languages : en
Pages : 396

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 Techniques and Applications

Large Deviations Techniques and Applications PDF Author: Amir Dembo
Publisher: Springer
ISBN: 9783642033100
Category : Science
Languages : en
Pages : 396

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 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

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 Techniques and Applications

Large Deviations Techniques and Applications PDF Author: Amir Dembo
Publisher: Springer
ISBN: 9781461253228
Category : Mathematics
Languages : en
Pages : 397

Book Description
Large deviation estimates have proved to be a crucial tool in statistics, engineering, statistical mechanics, and applied probability. This new edition presents an introduction to the theory of large deviations, with rigorous mathematical applications from a wide range of areas, including electrical engineering and DNA sequencing.

Large Deviations

Large Deviations PDF Author: Frank Hollander
Publisher: American Mathematical Soc.
ISBN: 9780821844359
Category : Mathematics
Languages : en
Pages : 164

Book Description
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

Large Deviations PDF Author: Jean-Dominique Deuschel and Daniel W. Stroock
Publisher: American Mathematical Soc.
ISBN: 9780821869345
Category : Mathematics
Languages : en
Pages : 296

Book Description
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

Large Deviations PDF Author: Jean-Dominique Deuschel
Publisher: American Mathematical Soc.
ISBN: 082182757X
Category : Mathematics
Languages : en
Pages : 298

Book Description
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 and Asymptotic Methods in Finance

Large Deviations and Asymptotic Methods in Finance PDF Author: Peter K. Friz
Publisher: Springer
ISBN: 3319116053
Category : Mathematics
Languages : en
Pages : 590

Book Description
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.

Large Deviations for Markov Chains

Large Deviations for Markov Chains PDF Author: Alejandro D. de Acosta
Publisher:
ISBN: 1009063359
Category : Mathematics
Languages : en
Pages : 264

Book Description
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.

A Weak Convergence Approach to the Theory of Large Deviations

A Weak Convergence Approach to the Theory of Large Deviations PDF Author: Paul Dupuis
Publisher: John Wiley & Sons
ISBN: 1118165896
Category : Mathematics
Languages : en
Pages : 504

Book Description
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.

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

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.