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A Weak Convergence Approach to the Theory of Large Deviations
Wiley 2011; US$ 202.00Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis--a consistent new approach The theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty.... more...
A History of the Central Limit Theorem
Springer 2010; US$ 119.99This 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...
Rare Event Simulation using Monte Carlo Methods
Wiley 2009; US$ 136.00In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication... more...
Self-Normalized Processes
Springer 2008; US$ 79.99Self-normalized processes are of common occurrence in probabilistic and statistical studies. This volume covers developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. It treats the theory and applications of self-normalization. more...
Large Deviations and Metastability
Cambridge University Press 2005; US$ 202.00The book provides a general introduction to the theory of large deviations and a wide overview of the metastable behaviour of stochastic dynamics. Written to be accessible to graduate students, this book provides an excellent route into contemporary research. more...
Information Theory And The Central Limit Theorem
World Scientific Publishing Company 2004; US$ 80.60This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from... more...
Large Deviations and Idempotent Probability
CRC Press 2001; US$ 139.95Noted researcher in the modern theory of large deviations, Puhalskii (mathematics, U. of Colorado-Denver) expounds on the recent methodology of building large deviation theory along the lines of weak convergence theory. He develops an idempotent, or maxitive, probability theory, and introduces maxingales as idempotent analogues of martingales, Wien more...
Uniform Central Limit Theorems
Cambridge University Press 1999; US$ 43.00This treatise by an acknowledged expert includes several topics not found in any previous book. more...
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