Probability Measures On Locally Compact Groups

Author : H. Heyer
Publisher : Springer Science & Business Media
ISBN 13 : 3642667066
Total Pages : 542 pages
Book Rating : 4.60/5 ( download)

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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.

Author : Herbert Heyer
Publisher :
ISBN 13 : 9780387083322
Total Pages : 531 pages
Book Rating : 4.24/5 ( download)

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Download or read book Ergebnisse der Mathematik und ihrer Grenzgebiete written by Herbert Heyer and published by . This book was released on 195? with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H. Heyer
Publisher : Springer
ISBN 13 : 3540354069
Total Pages : 366 pages
Book Rating : 4.62/5 ( download)

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Download or read book Probability Measures on Groups written by H. Heyer and published by Springer. This book was released on 2006-11-15 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Wilfried Hazod
Publisher :
ISBN 13 : 9789401730624
Total Pages : 636 pages
Book Rating : 4.28/5 ( download)

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Download or read book Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups written by Wilfried Hazod and published by . This book was released on 2014-01-15 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H. Heyer
Publisher : Springer
ISBN 13 : 3540392068
Total Pages : 492 pages
Book Rating : 4.64/5 ( download)

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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

Author : David Applebaum
Publisher : Springer
ISBN 13 : 3319078429
Total Pages : 217 pages
Book Rating : 4.27/5 ( download)

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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 217 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.

Author : Wilfried Hazod
Publisher : Springer Science & Business Media
ISBN 13 : 940173061X
Total Pages : 626 pages
Book Rating : 4.17/5 ( download)

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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.

Author : K. R. Parthasarathy
Publisher : Academic Press
ISBN 13 : 1483225259
Total Pages : 289 pages
Book Rating : 4.58/5 ( download)

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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.

Author : Herbert Heyer
Publisher : Springer
ISBN 13 : 3540448527
Total Pages : 397 pages
Book Rating : 4.25/5 ( download)

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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:

Author : H. Heyer
Publisher :
ISBN 13 : 9783662186558
Total Pages : 368 pages
Book Rating : 4.51/5 ( download)

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Download or read book Probability Measures on Groups written by H. Heyer and published by . This book was released on 2014-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: