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Sigma Series in Stochastics, Volume 1, 37--70
Heldermann Verlag 2004

Quantification in Stochastics and the Stability Concept

Vladimir Kalashnikov
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Quantitative aspects of some applied probabilistic results are considered. In particular, approximations given by classical limit theorems and two methods (Chen-Stein and probability metrics) disclosing accuracy of these approximations are discussed. Some widely used asymptotic formulae (mostly, from risk theory) are reviewed. It is shown that accuracy of these formulae is not satisfactory, in general, for practical purposes. A general stability concept for stochastic models, its role in quantification, and corresponding examples are discussed.