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#### Laws of Small Numbers

Springer 2010; US$ 89.95Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book... more...

#### A History of the Central Limit Theorem

Springer 2010; US$ 199.00This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace... more...

#### Sorting

Wiley 2011; US$ 198.00A cutting-edge look at the emerging distributional theory of sorting Research on distributions associated with sorting algorithms has grown dramatically over the last few decades, spawning many exact and limiting distributions of complexity measures for many sorting algorithms. Yet much of this information has been scattered in disparate and highly... more...

#### An Introduction to Heavy-Tailed and Subexponential Distributions

Springer 2011; US$ 99.00This monograph provides a complete and comprehensive introduction to the theory of long-tailed and subexponential distributions in one dimension. New results are presented in a simple, coherent and systematic way. All the standard properties of such convolutions are then obtained as easy consequences of these results. The book focuses on more theoretical... more...

#### Peacocks and Associated Martingales, with Explicit Constructions

Springer 2011; US$ 139.00We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In... more...

#### The Poisson-Dirichlet Distribution and Related Topics

Springer 2010; US$ 99.00The Poisson-Dirichlet distribution is an infinite dimensional probability distribution. It was introduced by Kingman over thirty years ago, and has found applications in a broad range of areas including Bayesian statistics, combinatorics, differential geometry, economics, number theory, physics, and population genetics. This monograph provides a comprehensive... more...

#### Wahrscheinlichkeitstheorie

Springer 2013; US$ 39.95Seit seinem Erscheinen hat sich das Buch umgehend als Standardwerk für eine umfassende und moderne Einführung in die Wahrscheinlichkeitstheorie und ihre maßtheoretischen Grundlagen etabliert. Themenschwerpunkte sind: Maß- und Integrationstheorie, Grenzwertsätze für Summen von Zufallsvariablen (Gesetze der Großen Zahl,... more...

#### Limit Theorems in Probability, Statistics and Number Theory

Springer 2013; US$ 139.00Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic... more...

#### Treasures Inside the Bell

World Scientific Publishing Company 2003; US$ 76.00Generalized versions of the central limit theorem that lead to Gaussian distributions over one and higher dimensions, via arbitrary iterations of simple mappings, have recently been discovered by the author of this publication and his collaborators. Treasures Inside the Bell: Hidden Order in Chance reveals how these new constructions result in infinite... more...

#### Stochastic Orders in Reliability and Risk

Springer 2013; US$ 129.00Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International... more...