A Weak Convergence Approach To The Theory Of Large Deviations PDF Download
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| Author | : Paul Dupuis |
| Publisher | : John Wiley & Sons |
| Total Pages | : 506 |
| Release | : 2011-09-09 |
| Genre | : Mathematics |
| ISBN | : 1118165896 |
Download A Weak Convergence Approach to the Theory of Large Deviations Book in PDF, ePub and Kindle
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.
| Author | : Paul Dupuis |
| Publisher | : John Wiley & Sons |
| Total Pages | : 522 |
| Release | : 1997-02-27 |
| Genre | : Mathematics |
| ISBN | : 9780471076728 |
Download A Weak Convergence Approach to the Theory of Large Deviations Book in PDF, ePub and Kindle
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.
| Author | : Paul Dupuis |
| Publisher | : Wiley-Interscience |
| Total Pages | : 504 |
| Release | : 1997-02-27 |
| Genre | : Mathematics |
| ISBN | : 9780471076728 |
Download A Weak Convergence Approach to the Theory of Large Deviations Book in PDF, ePub and Kindle
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.
| Author | : Anatolii Puhalskii |
| Publisher | : CRC Press |
| Total Pages | : 515 |
| Release | : 2001-05-07 |
| Genre | : Business & Economics |
| ISBN | : 1420035800 |
Download Large Deviations and Idempotent Probability Book in PDF, ePub and Kindle
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak
| Author | : Anatolii Puhalskii |
| Publisher | : CRC Press |
| Total Pages | : 520 |
| Release | : 2020-12-18 |
| Genre | : Large deviations |
| ISBN | : 9780367455293 |
Download Large Deviations and Idempotent Probability Book in PDF, ePub and Kindle
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle and well-known methods for establishing weak convergence results. In this monograph, Dr. Puhalskii expounds upon the recent methodology of building large deviation theory along the lines of weak convergence theory. The author develops an idempotent (or maxitive) probability theory, introduces idempotent analogues of martingales (maxingales), Wiener and Poisson processes, and Ito differential equations, and studies their properties. The large deviation principle for stochastic processes is formulated as a certain type of convergence of stochastic processes to idempotent processes. The author calls this large deviation convergence. The book features a wide range of topics, from the foundations of idempotent measure theory to large deviation asymptotics of semimartingales and Markov processes, in particular, those arising in the analysis of queueing systems. Large Deviations and Idempotent Probability offers an outstanding opportunity to examine both the development of a remarkable approach and recently discovered results as presented by one of the foremost leaders in the field. Book jacket.
| Author | : Amarjit Budhiraja |
| Publisher | : Springer |
| Total Pages | : 574 |
| Release | : 2019-08-10 |
| Genre | : Mathematics |
| ISBN | : 1493995790 |
Download Analysis and Approximation of Rare Events Book in PDF, ePub and Kindle
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
| Author | : Jin Feng |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 426 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821841459 |
Download Large Deviations for Stochastic Processes Book in PDF, ePub and Kindle
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 | : |
| Publisher | : Academic Press |
| Total Pages | : 329 |
| Release | : 1989-06-21 |
| Genre | : Mathematics |
| ISBN | : 0080874576 |
Download Large Deviations Book in PDF, ePub and Kindle
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).
| Author | : Frank Hollander |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 164 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780821844359 |
Download Large Deviations Book in PDF, ePub and Kindle
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 | : Adam Shwartz |
| Publisher | : CRC Press |
| Total Pages | : 576 |
| Release | : 1995-09-01 |
| Genre | : Mathematics |
| ISBN | : 9780412063114 |
Download Large Deviations For Performance Analysis Book in PDF, ePub and Kindle
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.
