Differentiable Measures And The Malliavin Calculus

Author : Vladimir Igorevich Bogachev
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 46,6 Mb
Release : 2010-07-21
Category : Mathematics
ISBN : 9780821849934

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Differentiable Measures and the Malliavin Calculus by Vladimir Igorevich Bogachev Pdf

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 : Vladimir Igorevich Bogachev
Publisher : Unknown
Page : 506 pages
File Size : 47,9 Mb
Release : 2014-05-21
Category : MATHEMATICS
ISBN : 1470413914

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Differentiable Measures and the Malliavin Calculus by Vladimir Igorevich Bogachev Pdf

Author : Marta Sanz-Sole
Publisher : CRC Press
Page : 172 pages
File Size : 48,8 Mb
Release : 2005-08-17
Category : Mathematics
ISBN : 9781439818947

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Malliavin Calculus with Applications to Stochastic Partial Differential Equations by Marta Sanz-Sole Pdf

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 present

Author : David Nualart
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 42,7 Mb
Release : 2006-02-27
Category : Mathematics
ISBN : 9783540283294

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The Malliavin Calculus and Related Topics by David Nualart Pdf

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 : Denis R. Bell
Publisher : Courier Corporation
Page : 124 pages
File Size : 50,8 Mb
Release : 2012-12-03
Category : Mathematics
ISBN : 9780486152059

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The Malliavin Calculus by Denis R. Bell Pdf

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 : Denis Bell
Publisher : CRC Press
Page : 134 pages
File Size : 40,8 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 058224689X

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Degenerate Stochastic Differential Equations and Hypoellipticity by Denis Bell Pdf

The main theme of this Monograph is the study of degenerate stochastic differential equations, considered as transformations of the Wiener measure, and their relationship with partial differential equations. The book contains an elementary derivation of Malliavin's integration by parts formula, a proof of the probabilistic form of Hormander's theorem, an extension of Hormander's theorem for infinitely degenerate differential operators, and criteria for the regularity of measures induced by stochastic hereditary-delay equations.

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
Page : 433 pages
File Size : 45,6 Mb
Release : 2015-01-26
Category : Electronic
ISBN : 9781470418694

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Gaussian Measures by Vladimir I. Bogachev Pdf

This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.

Author : Nicolai Victorovich Norin
Publisher : World Scientific
Page : 280 pages
File Size : 48,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9810225687

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The Extended Stochastic Integral in Linear Spaces with Differentiable Measures and Related Topics by Nicolai Victorovich Norin Pdf

This volume discusses the extended stochastic integral (ESI) (or Skorokhod-Hitsuda Integral) and its relation to the logarithmic derivative of differentiable measure along the vector or operator field. In addition, the theory of surface measures and the theory of heat potentials in infinite-dimensional spaces are discussed. These theories are closely related to ESI.It starts with an account of classic stochastic analysis in the Wiener spaces; and then discusses in detail the ESI for the Wiener measure including properties of this integral understood as a process. Moreover, the ESI with a nonrandom kernel is investigated.Some chapters are devoted to the definition and the investigation of properties of the ESI for Gaussian and differentiable measures.Surface measures in Banach spaces and heat potentials theory in Hilbert space are also discussed.

Author : Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov
Publisher : American Mathematical Society
Page : 495 pages
File Size : 49,5 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781470470098

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Fokker–Planck–Kolmogorov Equations by Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov Pdf

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Author : David Nualart,Eulalia Nualart
Publisher : Cambridge University Press
Page : 249 pages
File Size : 45,9 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781107039124

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Introduction to Malliavin Calculus by David Nualart,Eulalia Nualart Pdf

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Author : V.I. Bogachev,O.G. Smolyanov
Publisher : Springer
Page : 456 pages
File Size : 46,5 Mb
Release : 2017-05-16
Category : Mathematics
ISBN : 9783319571171

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Topological Vector Spaces and Their Applications by V.I. Bogachev,O.G. Smolyanov Pdf

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Author : Laurent Decreusefond
Publisher : Springer Nature
Page : 180 pages
File Size : 51,7 Mb
Release : 2022-06-23
Category : Mathematics
ISBN : 9783031013119

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Selected Topics in Malliavin Calculus by Laurent Decreusefond Pdf

This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all the results which are known even for the basic subjects which are addressed here. The goal was to give the largest possible variety of proof techniques. For instance, we did not focus on the proof of concentration inequality for functionals of the Brownian motion, as it closely follows the lines of the analog result for Poisson functionals. This book grew from the graduate courses I gave at Paris-Sorbonne and Paris-Saclay universities, during the last few years. It is supposed to be as accessible as possible for students who have knowledge of Itô calculus and some rudiments of functional analysis.

Author : Robert C. Dalang
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 42,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9783540859932

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A Minicourse on Stochastic Partial Differential Equations by Robert C. Dalang Pdf

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

Author : L. Accardi,C.C. Heyde
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461222248

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Probability Towards 2000 by L. Accardi,C.C. Heyde Pdf

Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.

Author : M M Rao
Publisher : World Scientific
Page : 576 pages
File Size : 54,9 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9789814551298

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Real and Stochastic Analysis by M M Rao Pdf

This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research. Contents:Gaussian Measures on Infinite Dimensional Spaces (V I Bogachev)Random Fields and Hypergroups (Herbert Heyer)A Concise Exposition of Large Deviations (F Hiai)Quantum White Noise Calculus and Applications (Un Cig Ji and Nobuaki Obata)Weak Radon–Nikodým Derivatives, Dunford–Schwartz Type Integration, and Cramér and Karhunen Processes (Yûichirô Kakihara)Entropy, SDE–LDP and Fenchel–Legendre–Orlicz Classes (M M Rao)Bispectral Density Estimation in Harmonizable Processes (H Soedjak) Readership: Graduate students and researchers in Probability and Stochastic Analysis. Keywords:Stochastic Measures;Stochastic Differential Equations;RSA-Current TrendsKey Features:The book covers new developments in Stochastic AnalysisThe research works contain detailed exposition to induce new researchers