Geometric Aspects of Probability Theory and Mathematical Statistics PDF Download

Author: V. V. Buldygin
Publisher:
ISBN: 9789401716888
Category :
Languages : en
Pages : 316

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Author: V.V. Buldygin
Publisher: Springer Science & Business Media
ISBN: 9780792364139
Category : Mathematics
Languages : en
Pages : 322

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Book Description
This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.

Author: V.V. Buldygin
Publisher: Springer Science & Business Media
ISBN: 9401716870
Category : Mathematics
Languages : en
Pages : 314

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Book Description
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.

Author: Ovidiu Calin
Publisher: Springer
ISBN: 3319077791
Category : Mathematics
Languages : en
Pages : 375

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Book Description
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Author: B. Grigelionis
Publisher: de Gruyter
ISBN: 9783112307892
Category : Mathematics
Languages : en
Pages : 0

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Author: B. Grigelionis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112314190
Category : Mathematics
Languages : en
Pages : 656

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No detailed description available for "GRIGELIONIS: PROCEEDINGS OF THE FIFTH VILNIUS CONFERE E-BOOK".

Author: Robert J. Adler
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 302

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Book Description

Author: Harald Cramér
Publisher: Krieger Publishing Company
ISBN:
Category : Probabilities
Languages : en
Pages : 300

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Book Description

Author: Aram Aruti?u?novich Sveshnikov
Publisher: Courier Corporation
ISBN: 9780486637174
Category : Mathematics
Languages : en
Pages : 516

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Book Description
Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

Author: Daniel A. Klain
Publisher: Cambridge University Press
ISBN: 9780521596541
Category : Mathematics
Languages : en
Pages : 196

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Book Description
Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santal and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove the fundamental theorem of integral geometry, namely, the kinematic formula. Finally, the analogies between invariant measures on polyconvex sets and measures on order ideals of finite partially ordered sets are investigated. The relationship between convex geometry and enumerative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems.