Author: Wilfried Hazod
Publisher:
ISBN: 9789401730624
Category :
Languages : en
Pages : 636

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Book Description

Author: Wilfried Hazod
Publisher: Springer Science & Business Media
ISBN: 940173061X
Category : Mathematics
Languages : en
Pages : 626

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Book Description
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: H. Heyer
Publisher: Springer Science & Business Media
ISBN: 3642667066
Category : Mathematics
Languages : en
Pages : 542

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Book Description
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: H. Heyer
Publisher: Springer
ISBN: 9783540091240
Category : Mathematics
Languages : de
Pages : 352

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Book Description

Author: H. Heyer
Publisher: Springer
ISBN: 3540392068
Category : Mathematics
Languages : de
Pages : 492

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Book Description
a

Author: H. Heyer
Publisher: Springer
ISBN: 3540354069
Category : Mathematics
Languages : de
Pages : 366

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Book Description

Author: K. R. Parthasarathy
Publisher: American Mathematical Soc.
ISBN: 082183889X
Category : Mathematics
Languages : en
Pages : 290

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Book Description
Presents an account of the theory of probability measures on complete metric spaces. This title includes a description of the basics of topology on the set of measures. It discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems.

Author: Herbert Heyer
Publisher:
ISBN:
Category :
Languages : de
Pages :

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Author: H. Heyer
Publisher: Springer
ISBN: 9781489923660
Category : Mathematics
Languages : en
Pages : 498

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Book Description
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".

Author: Herbert Heyer
Publisher: Springer
ISBN: 3540462066
Category : Mathematics
Languages : en
Pages : 446

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Book Description
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.