Drawing on his own research over the past 21 years, Anastassiou (mathematical sciences, U. of Memphis, Tennessee) presents univariate and multivariate probabilistic inequalities regarding basic probabilistic entities like expectation, variance, moment generating function, and covariance. The chapters are self-contained, he says, and several advanced courses could be taught using it. The topics include basic stochastic Ostrowski inequalities, Grothendieck inequalities, the sharp high degree estimation of Csiszr's f-divergence, a general discrete measure of dependence, extreme bounds on the average of rounded off observation under a moment condition, precise rates of Prokhorov convergence using three moment conditions, geometric moment methods applied to optimal portfolio, an expansion formula, and integration by parts on the multidimensional domain. Annotation �2010 Book News, Inc., Portland, OR (booknews.com)

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"The book is a useful source for references to many results which are not covered by numerous books well-known in Probability Theory. The book under consideration is addressed to the researchers and graduate students. It could be employed to prepare special courses and also to discuss the material at the research seminars." --Zentralblatt MATH

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