Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Download or read book Probability on Compact Lie Groups written by David Applebaum and published by Springer. This book was released on 2014-06-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.

Download or read book Probability Measures on Groups X written by H. Heyer and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".

Download or read book Probability Measures on Groups written by H. Heyer and published by Springer. This book was released on 2006-11-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: a

Download or read book Probability Measure on Groups VII written by H. Heyer and published by Springer. This book was released on 2006-11-14 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Measures on Groups written by Herbert Heyer and published by Springer. This book was released on 1979 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Measures on Groups IX written by Herbert Heyer and published by Springer. This book was released on 2006-11-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest in this series of Oberwolfach conferences focussed on the interplay between structural probability theory and various other areas of pure and applied mathematics such as Tauberian theory, infinite-dimensional rotation groups, central limit theorems, harmonizable processes, and spherical data. Thus it was attended by mathematicians whose research interests range from number theory to quantum physics in conjunction with structural properties of probabilistic phenomena. This volume contains 5 survey articles submitted on special invitation and 25 original research papers.

Download or read book Probability Measures on Groups VIII written by Herbert Heyer and published by Springer. This book was released on 2006-11-14 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups written by Wilfried Hazod and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups.

Download or read book Introduction to Probability and Measure written by K.R. Parthasarathy and published by Springer. This book was released on 2005-05-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account.

Download or read book Probability Measures on Metric Spaces written by K. R. Parthasarathy and published by Academic Press. This book was released on 2014-07-03 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.

Download or read book Probability Measures on Groups VII written by Herbert Heyer and published by Springer. This book was released on 1984 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Measures on Semigroups Convolution Products Random Walks and Random Matrices written by Göran Högnäs and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Scientific American article on chaos, see Crutchfield et al. (1986), illus trates a very persuasive example of recurrence. A painting of Henri Poincare, or rather a digitized version of it, is stretched and cut to produce a mildly distorted image of Poincare. The same procedure is applied to the distorted image and the process is repeated over and over again on the successively more and more blurred images. After a dozen repetitions nothing seems to be left of the original portrait. Miraculously, structured images appear briefly as we continue to apply the distortion procedure to successive images. After 241 iterations the original picture reappears, unchanged! Apparently the pixels of the Poincare portrait were moving about in accor dance with a strictly deterministic rule. More importantly, the set of all pixels, the whole portrait, was transformed by the distortion mechanism. In this exam ple the transformation seems to have been a reversible one since the original was faithfully recreated. It is not very farfetched to introduce a certain amount of randomness and irreversibility in the above example. Think of a random miscoloring of some pixels or of inadvertently giving a pixel the color of its neighbor. The methods in this book are geared towards being applicable to the asymp totics of such transformation processes. The transformations form a semigroup in a natural way; we want to investigate the long-term behavior of random elements of this semigroup.

Download or read book Probabilities on the Heisenberg Group written by Daniel Neuenschwander and published by Springer. This book was released on 2006-11-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.

Download or read book Probability Space written by Nancy Kress and published by Macmillan. This book was released on 2004-01-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nancy Kress cemented her reputation in SF with the publication of her multiple-award–winning novella, “Beggars in Spain,” which became the basis for her extremely successful Beggars Trilogy (comprising Beggars in Spain, Beggars and Choosers, and Beggars Ride). And now she brings us Probability Space, the conclusion of the trilogy that began with Probability Moon and then Probability Sun, which is centered on the same world as Kress’s Nebula Award-winning novelette, “Flowers of Aulit Prison.” The Probability Trilogy has already been widely recognized as the next great work by this important SF writer. In Probability Space, humanity’s war with the alien Fallers continues, and it is a war we are losing. Our implacable foes ignore all attempts at communication, and they take no prisoners. Our only hope lies with an unlikely coalition: Major Lyle Kaufman, retired warrior; Marbet Grant, the Sensitive who’s involved with Kaufman; Amanda, a very confused fourteen-year-old girl; and Magdalena, one of the biggest power brokers in all of human space. As the action moves from Earth to Mars to the farthest reaches of known space, with civil unrest back home and alien war in deep space, four humans--armed with little more than an unproven theory--try to enter the Fallers’ home star system. It’s a desperate gamble, and the fate of the entire universe may hang in the balance.

Download or read book Analysis On Infinite dimensional Lie Groups And Algebras Proceedings Of The International Colloquium written by Jean Marion and published by World Scientific. This book was released on 1998-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.

Download or read book Probability Measures on Semigroups written by Göran Högnäs and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.