Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups
DOWNLOAD
Download Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups
DOWNLOAD
Author : Gennadiĭ Mikhaĭlovich Felʹdman
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramer theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Feldman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods because of the absence of a natural analytic structure on the dual group, which is the domain of characteristic functions. Nevertheless, the methods developed in this book allow one to apply analytic techniques in the algebraic setting. The first part of the book presents results on the arithmetic of probability distributions of random variables with values in a locally compact abelian group. The second part studies problems of characterization of a Gaussian distribution of a locally compact abelian group by the independence or identical distribution of its linear statistics.
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups
DOWNLOAD
Author : Gennadij M. Fel'dman
language : en
Publisher: American Mathematical Soc.
Release Date :
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups written by Gennadij M. Fel'dman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups
DOWNLOAD
Author : Gennadĭ Mikaĭlovich Felʹdman
language : en
Publisher:
Release Date : 1993
Arithmetic Of Probability Distributions And Characterization Problems On Abelian Groups written by Gennadĭ Mikaĭlovich Felʹdman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Abelian groups categories.
This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramér theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Fel′′′dman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods because of the absence of a natural analytic structure on the dual group, which is the domain of characteristic functions. Nevertheless, the methods developed in this book allow one.
Functional Equations And Characterization Problems On Locally Compact Abelian Groups
DOWNLOAD
Author : Gennadiĭ Mikhaĭlovich Felʹdman
language : en
Publisher: European Mathematical Society
Release Date : 2008
Functional Equations And Characterization Problems On Locally Compact Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Abelian groups categories.
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.
Characterization Of Probability Distributions On Locally Compact Abelian Groups
DOWNLOAD
Author : Gennadiy Feldman
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
Characterization Of Probability Distributions On Locally Compact Abelian Groups written by Gennadiy Feldman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
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.
Tangents And Secants Of Algebraic Varieties
DOWNLOAD
Author : F. L. Zak
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Tangents And Secants Of Algebraic Varieties written by F. L. Zak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
"The book is devoted to geometry of algebraic varieties in projective spaces. Among the objects considered in some detail are tangent and secant varieties, Gauss maps, dual varieties, hyperplane sections, projections, and varieties of small codimension. Emphasis is made on the study of interplay between irregular behavior of (higher) secant varieties and irregular tangencies to the original variety. Classification of varieties with unusual tangential properties yields interesting examples many of which arise as orbits of representations of algebraic groups."--ABSTRACT.
Complexity Of Proofs And Their Transformations In Axiomatic Theories
DOWNLOAD
Author : V. P. Orevkov
language : en
Publisher: American Mathematical Soc.
Release Date :
Complexity Of Proofs And Their Transformations In Axiomatic Theories written by V. P. Orevkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This book develops the tool of logical deduction schemata by using it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories.
An Introduction To Sato S Hyperfunctions
DOWNLOAD
Author : Mitsuo Morimoto
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
An Introduction To Sato S Hyperfunctions written by Mitsuo Morimoto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.
Elie Cartan 1869 1951
DOWNLOAD
Author : M. A. Akivis
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-14
Elie Cartan 1869 1951 written by M. A. Akivis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-14 with Mathematics categories.
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
Control Of Systems With Aftereffect
DOWNLOAD
Author : Vladimir Borisovich Kolmanovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-01-01
Control Of Systems With Aftereffect written by Vladimir Borisovich Kolmanovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Computers categories.
Deterministic and stochastic control systems with aftereffect are considered. Necessary and sufficient conditions for the optimality of such systems are obtained. Various methods for the construction of exact and approximate solutions of optimal control problems are suggested. Problems of adaptive control for systems with aftereffect are analyzed. Numerous applications are described. The book can be used by researchers, engineers, and graduate students working in optimal control theory and various applications.