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Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups
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Book Synopsis Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by : Gennadiĭ Mikhaĭlovich Felʹdman
Download or read book Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and published by American Mathematical Soc.. This book was released on 1993 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Book Synopsis Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by : Gennadij M. Fel'dman
Download or read book Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups written by Gennadij M. Fel'dman and published by American Mathematical Soc.. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Book Synopsis Characterization of Probability Distributions on Locally Compact Abelian Groups by : Gennadiy Feldman
Download or read book Characterization of Probability Distributions on Locally Compact Abelian Groups written by Gennadiy Feldman and published by American Mathematical Society. This book was released on 2023-04-07 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.
Author :Gennadiĭ Mikhaĭlovich Felʹdman Publisher :European Mathematical Society ISBN 13 :9783037190456 Total Pages :272 pages Book Rating :4.1/5 (94 download)
Book Synopsis Functional Equations and Characterization Problems on Locally Compact Abelian Groups by : Gennadiĭ Mikhaĭlovich Felʹdman
Download or read book Functional Equations and Characterization Problems on Locally Compact Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and published by European Mathematical Society. This book was released on 2008 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group $X$. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac-Bernstein, Skitovich-Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of $X$. Group analogs of the Cramer and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory.
Book Synopsis Probability Theory by : Anatoli_ I_A_kovlevich Dorogovt_s_ev
Download or read book Probability Theory written by Anatoli_ I_A_kovlevich Dorogovt_s_ev and published by American Mathematical Soc.. This book was released on 2011-06-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.
Book Synopsis Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications by : Mark Lʹvovich Agranovskiĭ
Download or read book Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications written by Mark Lʹvovich Agranovskiĭ and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.
Book Synopsis Structural Aspects in the Theory of Probability by : Herbert Heyer
Download or read book Structural Aspects in the Theory of Probability written by Herbert Heyer and published by World Scientific. This book was released on 2004 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the algebraic-topological aspects of probabilitytheory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroupsand the corresponding processes with independent increments
Book Synopsis Mathematics of Fractals by : Masaya Yamaguchi
Download or read book Mathematics of Fractals written by Masaya Yamaguchi and published by American Mathematical Soc.. This book was released on 1997 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at providing a handy explanation of the notions behind the self-similar sets called "fractals" and "chaotic dynamical systems". The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass's) and chaotic dynamical systems; these nowhere-differentiable functions are generating functions of chaotic dynamical systems. These functions are shown to be in a sense unique solutions of certain boundary problems. The last chapter of the book treats harmonic functions on fractal sets.
Book Synopsis Nontraditional methods in mathematical hydrodynamics by : O. V. Troshkin
Download or read book Nontraditional methods in mathematical hydrodynamics written by O. V. Troshkin and published by American Mathematical Soc.. This book was released on 1995-03-16 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary Navier-Stokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair one-point velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.
Author :Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina Publisher :American Mathematical Soc. ISBN 13 :9780821897836 Total Pages :208 pages Book Rating :4.8/5 (978 download)
Book Synopsis Local Properties of Distributions of Stochastic Functionals by : Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina
Download or read book Local Properties of Distributions of Stochastic Functionals written by Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina and published by American Mathematical Soc.. This book was released on 1998-02-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes. Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.
Book Synopsis Applications of Hypergroups and Related Measure Algebras by :
Download or read book Applications of Hypergroups and Related Measure Algebras written by and published by American Mathematical Soc.. This book was released on 1995-02-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: `The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.
Book Synopsis Methods for Analysis of Nonlinear Elliptic Boundary Value Problems by : I. V. Skrypnik
Download or read book Methods for Analysis of Nonlinear Elliptic Boundary Value Problems written by I. V. Skrypnik and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Book Synopsis Discreteness and Continuity in Problems of Chaotic Dynamics by : Michael L. Blank
Download or read book Discreteness and Continuity in Problems of Chaotic Dynamics written by Michael L. Blank and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the study of ergodic properties of so-called chaotic dynamical systems. One of the central topics is the interplay between deterministic and quasi-stochastic behaviour in chaotic dynamics and between properties of continuous dynamical systems and those of their discrete approximations. Using simple examples, the author describes the main phenomena known in chaotic dynamical systems, studying topics such as the operator approach in chaotic dynamics, stochastic stability, and the so-called coupled systems. The last two chapters are devoted to problems of numerical modeling of chaotic dynamics.
Book Synopsis Compact Lie Groups and Their Representations by : Dmitriĭ Petrovich Zhelobenko
Download or read book Compact Lie Groups and Their Representations written by Dmitriĭ Petrovich Zhelobenko and published by American Mathematical Soc.. This book was released on 1973-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Problems and Theorems in Linear Algebra by : Viktor Vasil_evich Prasolov
Download or read book Problems and Theorems in Linear Algebra written by Viktor Vasil_evich Prasolov and published by American Mathematical Soc.. This book was released on 1994-06-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.
Book Synopsis Infinite-Dimensional Lie Groups by : Hideki Omori
Download or read book Infinite-Dimensional Lie Groups written by Hideki Omori and published by American Mathematical Soc.. This book was released on 2017-11-07 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.
Book Synopsis Groups, Generators, Syzygies, and Orbits in Invariant Theory by : V. L. Popov
Download or read book Groups, Generators, Syzygies, and Orbits in Invariant Theory written by V. L. Popov and published by American Mathematical Soc.. This book was released on 2011-01-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
