Theory Of Characteristic Functions And The Classical Moment Problem
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Characteristic Functions and Moment Sequences
Author | : Torben Maack Bisgaard |
Publisher | : Nova Publishers |
Total Pages | : 152 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9781560728603 |
This book contains basic information on characteristic functions and moment sequences that is frequently used in probability theory. Characteristic functions and moment sequences are viewed as special cases of positive definite functions. Positive definite functions occur in diverse parts of mathematics, e.g. in operator theory, moment problems, complex function theory, embedding problems, integral equations, and other areas. However, the area of mathematics in which the largest number of people use positive definite functions (some without knowing it) seems to be that of probability theory.
The Classical Moment Problem
Author | : N. I. Akhiezer |
Publisher | : Courier Dover Publications |
Total Pages | : 273 |
Release | : 2020-12-16 |
Genre | : Mathematics |
ISBN | : 0486845559 |
This text provides a classic treatment of issues associated with the moment problem that also involve linear algebra, probability theory, stochastic processes, quantum fields, signal processing, and more. 1965 edition.
A History of the Central Limit Theorem
Author | : Hans Fischer |
Publisher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2010-10-08 |
Genre | : Mathematics |
ISBN | : 0387878572 |
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Multivariate Characteristic and Correlation Functions
Author | : Zoltán Sasvári |
Publisher | : Walter de Gruyter |
Total Pages | : 376 |
Release | : 2013-03-22 |
Genre | : Mathematics |
ISBN | : 3110223996 |
In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.
Developments in Characteristic Function Theory
Author | : Eugene Lukacs |
Publisher | : Oxford University Press, USA |
Total Pages | : 190 |
Release | : 1987-03-01 |
Genre | : Characteristic functions |
ISBN | : 9780195205770 |
The general theory covered in this volume includes many new results and the author makes an important correction to previously held views on unimodality. Extensive new material is included on analytic distribution functions, ridge functions, and functions of bounded variation.
Applications of Characteristic Functions
Author | : Eugene Lukacs |
Publisher | : |
Total Pages | : 208 |
Release | : 1964 |
Genre | : Characteristic functions |
ISBN | : |
Topics in Probability
Author | : Narahari Prabhu |
Publisher | : World Scientific |
Total Pages | : 94 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814335487 |
Recent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.
System Theory, the Schur Algorithm and Multidimensional Analysis
Author | : Daniel Alpay |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2007-03-20 |
Genre | : Mathematics |
ISBN | : 3764381361 |
This volume contains six peer-refereed articles written on the occasion of the workshop Operator theory, system theory and scattering theory: multidimensional generalizations and related topics, held at the Department of Mathematics of the Ben-Gurion University of the Negev in June, 2005. The book will interest a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Topics In Probability
Author | : Narahari U Prabhu |
Publisher | : World Scientific |
Total Pages | : 94 |
Release | : 2011-07-29 |
Genre | : Mathematics |
ISBN | : 981446225X |
Recent research in probability has been concerned with applications such as data mining and finance models. Some aspects of the foundations of probability theory have receded into the background. Yet, these aspects are very important and have to be brought back into prominence.