Inequalities In Analysis And Probability

The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail.

• Preliminaries
• Inequalities for Means and Integrals
• Analytic Inequalities
• Inequalities for Martingales
• Functional Inequalities
• Inequalities for Processes
• Inequalities in Complex Spaces
• Appendix A: Probability