eBook PDF Download Digital Library
Author: Ulf Grenander
Publisher: Courier Corporation
Published: 2008-01-01
Total Pages: 222
ISBN-13: 0486462870
DOWNLOAD EBOOK →This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.
Author: Gregory Budzban
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 250
ISBN-13: 0821820273
DOWNLOAD EBOOK →This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.
Author: Harold Andrew Elliott
Publisher: Holt, Rinehart and Winston of Canada c1966.
Published: 1966
Total Pages: 290
ISBN-13:
DOWNLOAD EBOOK →Author: Herbert Heyer
Publisher: World Scientific
Published: 2004-08-23
Total Pages: 399
ISBN-13: 981448217X
DOWNLOAD EBOOK →This book focuses on the algebraic-topological aspects of probability theory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that of the Fourier transform. This analytic tool along with the relevant parts of harmonic analysis makes it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. Graduate students, lecturers and researchers may use the book as a primer in the theory of probability measures on groups and related structures.This book has been selected for coverage in:• CC / Physical, Chemical & Earth Sciences• Index to Scientific Book Contents® (ISBC)
Author: Juerg Kohlas
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 274
ISBN-13: 1447100093
DOWNLOAD EBOOK →Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.
Author: H. A. (Harold Andrew) Elliott
Publisher: Holt, Rinehart and Winston of Canada
Published: 1967
Total Pages: 125
ISBN-13:
DOWNLOAD EBOOK →Author: P. Feinsilver
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 232
ISBN-13: 9401116482
DOWNLOAD EBOOK →This series presents some tools of applied mathematics in the areas of proba bility theory, operator calculus, representation theory, and special functions used currently, and we expect more and more in the future, for solving problems in math ematics, physics, and, now, computer science. Much of the material is scattered throughout available literature, however, we have nowhere found in accessible form all of this material collected. The presentation of the material is original with the authors. The presentation of probability theory in connection with group represen tations is new, this appears in Volume I. Then the applications to computer science in Volume II are original as well. The approach found in Volume III, which deals in large part with infinite-dimensional representations of Lie algebras/Lie groups, is new as well, being inspired by the desire to find a recursive method for calcu lating group representations. One idea behind this is the possibility of symbolic computation of the matrix elements. In this volume, Representations and Probability Theory, we present an intro duction to Lie algebras and Lie groups emphasizing the connections with operator calculus, which we interpret through representations, principally, the action of the Lie algebras on spaces of polynomials. The main features are the connection with probability theory via moment systems and the connection with the classical ele mentary distributions via representation theory. The various systems of polynomi als that arise are one of the most interesting aspects of this study.
