Inequalities in Analysis and Probability

The book is complementary to the classical courses on vector and functional Hilbert spaces, integration theory and probability which focus on inequalities; The preliminary chapter introduces most classical inequalities which are generalized to more complex models with detailed proofs; It covers different domains from existing books and contains many new results; It gathers inequalities from several domains of mathematics which are not generally presented together, in a unified approach; The topics include many stochastic processes with specific inequalities and the basis of the stochastic calculus is developed in numerous applications--