Large Deviations And The Malliavin Calculus
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Large Deviations And The Malliavin Calculus
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Author : Jean-Michel Bismut
language : en
Publisher: Birkhäuser
Release Date : 1984
Large Deviations And The Malliavin Calculus written by Jean-Michel Bismut and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Juvenile Nonfiction categories.
Large Deviations And Asymptotic Methods In Finance
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Author : Peter K. Friz
language : en
Publisher: Springer
Release Date : 2015-06-16
Large Deviations And Asymptotic Methods In Finance written by Peter K. Friz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-16 with Mathematics categories.
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
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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 And Applications
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Author : S. R. S. Varadhan
language : en
Publisher: SIAM
Release Date : 1984-01-01
Large Deviations And Applications written by S. R. S. Varadhan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
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.
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 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.
Stochastic Analysis And Related Topics Vii
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Author : Laurent Decreusefond
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Analysis And Related Topics Vii written by Laurent Decreusefond 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.
One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.
Large Deviations
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Author : Jean-Dominique Deuschel and Daniel W. Stroock
language : en
Publisher: American Mathematical Soc.
Release Date :
Large Deviations written by Jean-Dominique Deuschel and Daniel W. Stroock 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 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 :
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).
Large Deviations
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Author : S. R. S. Varadhan
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-08
Large Deviations written by S. R. S. Varadhan 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 2016-12-08 with Large deviations categories.
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.