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SSS 01
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Sigma Series
in Stochastics
SSS Volume 1
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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.
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