Author: Vladimir Igorevich Bogachev
Publisher: American Mathematical Soc.
ISBN: 082184993X
Category : Mathematics
Languages : en
Pages : 506
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Book Description
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:
ISBN: 9781470413910
Category : MATHEMATICS
Languages : en
Pages : 506
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Book Description
Author: Marta Sanz-Sole
Publisher: CRC Press
ISBN: 1439818940
Category : Mathematics
Languages : en
Pages : 172
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Book Description
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
ISBN: 3540283293
Category : Mathematics
Languages : en
Pages : 390
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Book Description
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
ISBN: 0486152057
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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
ISBN: 9780582246898
Category : Mathematics
Languages : en
Pages : 134
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Book Description
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: David Nualart
Publisher: Cambridge University Press
ISBN: 1107039126
Category : Business & Economics
Languages : en
Pages : 249
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Book Description
A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.
Author: Vladimir I. Bogachev
Publisher: American Mathematical Soc.
ISBN: 147041869X
Category :
Languages : en
Pages : 433
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Book Description
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
ISBN: 9789810225681
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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
Publisher: American Mathematical Society
ISBN: 1470470098
Category : Mathematics
Languages : en
Pages : 495
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Book Description
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.
