V.V. Buldygin's Books

Geometric Aspects of Probability Theory and Mathematical Statistics

By: V.V. Buldygin,A.B. Kharazishvili

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Geometric Aspects of Probability Theory and Mathematical Statistics

By: V.V. Buldygin,A.B. Kharazishvili

It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.

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Page Count

314

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401716870

ISBN 13

9789401716871

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

By: V.V. Buldygin,Serguei Solntsev

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Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

By: V.V. Buldygin,Serguei Solntsev

Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.

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Page Count

512

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401155682

ISBN 13

9789401155687

Geometry

By: V. V. Prasolov, V. M. Tikhomirov

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Geometry

By: V. V. Prasolov, V. M. Tikhomirov

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

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Page Count

274

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470425432

ISBN 13

9781470425432

Boolean Functions in Coding Theory and Cryptography

By: Oleg A. Logachev,Alekse_ Aleksandrovich Sal_nikov,V. V. I_A_shchenko

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Boolean Functions in Coding Theory and Cryptography

By: Oleg A. Logachev,Alekse_ Aleksandrovich Sal_nikov,V. V. I_A_shchenko

This book offers a systematic presentation of cryptographic and code-theoretic aspects of the theory of Boolean functions. Both classical and recent results are thoroughly presented. Prerequisites for the book include basic knowledge of linear algebra, group theory, theory of finite fields, combinatorics, and probability. The book can be used by research mathematicians and graduate students interested in discrete mathematics, coding theory, and cryptography.

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Page Count

352

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821846809

ISBN 13

9780821846803

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

By: V.V. Buldygin,Serguei Solntsev

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Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

By: V.V. Buldygin,Serguei Solntsev

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Solve jigsaw puzzle

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Page Count

512

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401155682

ISBN 13

9789401155687

Book's by V.V. Buldygin

Geometric Aspects of Probability Theory and Mathematical Statistics

Geometric Aspects of Probability Theory and Mathematical Statistics

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

Geometry

Geometry

Boolean Functions in Coding Theory and Cryptography

Boolean Functions in Coding Theory and Cryptography

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

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