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Author : Jean-Michel Bismut
Publisher : Birkhäuser
Page : 238 pages
File Size : 50,6 Mb
Release : 1984
Category : Juvenile Nonfiction
ISBN : UOM:39015017340681
Author : Peter K. Friz,Jim Gatheral,Archil Gulisashvili,Antoine Jacquier,Josef Teichmann
Publisher : Springer
Page : 590 pages
File Size : 45,7 Mb
Release : 2015-06-16
Category : Mathematics
ISBN : 9783319116051
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.
Author : Jean-Dominique Deuschel,Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 40,5 Mb
Release : 2001
Category : Large deviations
ISBN : 9780821827574
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).
Author : Jean-Dominique Deuschel and Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 40,6 Mb
Release : 2024-07-03
Category : Large deviations
ISBN : 0821869345
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).
Author : S. R. S. Varadhan
Publisher : SIAM
Page : 80 pages
File Size : 42,5 Mb
Release : 1984-01-01
Category : Mathematics
ISBN : 1611970245
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.
Author : Amir Dembo,Ofer Zeitouni
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 49,5 Mb
Release : 2009-11-03
Category : Science
ISBN : 9783642033117
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.
Author : Denis R. Bell
Publisher : Courier Corporation
Page : 124 pages
File Size : 49,5 Mb
Release : 2012-12-03
Category : Mathematics
ISBN : 9780486152059
This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.
Author : Vladimir Igorevich Bogachev
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 42,9 Mb
Release : 2010-07-21
Category : Mathematics
ISBN : 9780821849934
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Author : Marta Sanz Solé
Publisher : EPFL Press
Page : 184 pages
File Size : 41,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 2940222061
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself b.
Author : David Nualart
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 50,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847794
The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.
Author : Frederi Viens,Jin Feng,Yaozhong Hu,Eulalia Nualart
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 55,5 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9781461459064
The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.
Author : David Nualart
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 52,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781475724370
The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.
Author : David Nualart
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 46,6 Mb
Release : 2006-02-27
Category : Mathematics
ISBN : 9783540283294
The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.
Author : Frank Hollander
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 50,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0821844350
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 : Anonim
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 52,6 Mb
Release : 2010-02-15
Category : Mathematics
ISBN : 9783642113888
The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. The 7th issue of the Transactions on Computational Science journal is devoted to core computational science techniques, such as grid computing, advanced numerical methods, and stochastic systems. It has been divided into two parts. The five papers in Part I focus on computations of stochastic systems and the four papers in Part II focus on computational methods for complex systems.