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Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups - Structural Properties and Limit Theorems (Hardcover, 2001 ed.)
Loot Price: R3,406
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Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups - Structural Properties and Limit Theorems (Hardcover, 2001 ed.)
Series: Mathematics and Its Applications, 531
Expected to ship within 10 - 15 working days
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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.
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