{"product_id":"9781402000409","title":"Mathematics and Its Applications: Structural Properties and Limit Theorems","description":"\u003ch1\u003eMathematics and Its Applications: Structural Properties and Limit Theorems\u003c\/h1\u003e \u003ch2\u003eHazod, Wilfried; Siebert, Eberhard\u003c\/h2\u003e \u003cp\u003eGeneralising 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 \u003cem\u003econtractable  groups\u003c\/em\u003e and - at least within the class of connected groups  - to \u003cem\u003ehomogeneous groups\u003c\/em\u003e, 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. \u003cbr\u003e  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. \u003cbr\u003e  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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2001-09-30\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9781402000409\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-017-3061-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 612\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46539684348044,"sku":"9781402000409","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781402000409.jpg?v=1775678871","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781402000409","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}