Vladimir Igorevich Bogachev's Books

Gaussian Measures

By: Vladimir Igorevich Bogachev

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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.

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Page Count

449

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810545

ISBN 13

9780821810545

Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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.

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Page Count

506

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184993X

ISBN 13

9780821849934

Gaussian Measures

By: Vladimir Igorevich Bogachev

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Gaussian Measures

By: Vladimir Igorevich Bogachev

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Page Count

449

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810545

ISBN 13

9780821810545

Measure Theory

By: Vladimir I. Bogachev

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Measure Theory

By: Vladimir I. Bogachev

This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

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Page Count

1075

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540345140

ISBN 13

9783540345145

Fokker-Planck-Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

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Fokker-Planck-Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

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.

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Page Count

495

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470425580

ISBN 13

9781470425586

Weak Convergence of Measures

By: Vladimir I. Bogachev

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Weak Convergence of Measures

By: Vladimir I. Bogachev

This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

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Page Count

302

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147044738X

ISBN 13

9781470447380

Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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Solve jigsaw puzzle

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Page Count

506

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184993X

ISBN 13

9780821849934

Book's by Vladimir Igorevich Bogachev

Gaussian Measures

Gaussian Measures

Differentiable Measures and the Malliavin Calculus

Differentiable Measures and the Malliavin Calculus

Gaussian Measures

Gaussian Measures

Measure Theory

Measure Theory

Fokker-Planck-Kolmogorov Equations

Fokker-Planck-Kolmogorov Equations

Weak Convergence of Measures

Weak Convergence of Measures

Differentiable Measures and the Malliavin Calculus

Differentiable Measures and the Malliavin Calculus

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