Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural Properties and Limit Theorems by Wilfried HazodStable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural Properties and Limit Theorems by Wilfried Hazod

Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural…

byWilfried Hazod, Eberhard Siebert

Paperback | December 15, 2010

Pricing and Purchase Info

$215.41 online 
$245.95 list price save 12%
Earn 1077 plum® points
Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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.
Title:Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups: Structural…Format:PaperbackDimensions:629 pages, 9.25 × 6.1 × 0.03 inPublished:December 15, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:904815832X

ISBN - 13:9789048158324

Look for similar items by category:

Reviews

Table of Contents

Preface. Introduction. I. Probabilities on vector spaces. II. Probabilities on simply connected nilpotent Lie groups. III. (Semi-) stability and limit theorems on general locally compact groups. Epilogue. Bibliography. List of Symbols. Index.

Editorial Reviews

`...a useful addition to the literature... valuable source of information for the specialists and for those trying to understand some aspects of stability and limit theorems on groups. ... contains an excellent bibliograpy and the authors have included pointers to related developments that are not treated in detail in the text.' Jahresbericht der Deutschen Mathematiker-Vereinigung, 105:2 (2003)