Probabilistic Inequalities

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 c2010 Book News, Inc., Portland, OR (booknews.com)