This volume contains 15 articles based on invited talks given at an AMS Special Session on 'Stochastic Inequalities and Their Applications' held at Georgia Institute of Technology (Atlanta). The session drew international experts who exchanged ideas and presented state-of-the-art results and techniques in the field. Together, the articles in the book give a comprehensive picture of this area of mathematical probability and statistics.The book includes new results on the following: convexity inequalities for ranges of vector measures; inequalities for tails of Gaussian chaos and for independent symmetric random variables; Bonferroni-type inequalities for sums of stationary sequences; Rosenthal-type second moment inequalities; variance inequalities for functions of multivariate random variables; correlation inequalities for stable random vectors; maximal inequalities for VC classes; deviation inequalities for martingale polynomials; and, expectation equalities for bounded mean-zero Gaussian processes. Various articles in the book emphasize applications of stochastic inequalities to hypothesis testing, mathematical finance, statistics, and mathematical physics.
Bounds on the non-convexity of ranges of vector measures with atoms by P. C. Allaart The class of Gaussian chaos of order two is closed by taking limits in distribution by M. A. Arcones Two inequalities and some applications in connection with $\rho*$-mixing, a survey by R. C. Bradley Variance inequalities for functions of multivariate random variables by W.-Y. Chang and D. St. P. Richards A note on sums of independent random variables by P. Hitczenko and S. Montgomery-Smith Exponential integrability of diffusion processes by Y. Hu Local dependencies in random fields via a Bonferroni-type inequality by A. Jakubowski and J. Rosinski Pricing-differentials and bounds for lookback options, and prophet problems in probability by R. P. Kertz A correlation inequality for stable random vectors by A. Koldobsky A note on the maximal inequalities for VC classes by R. Latala Comparison of moments via Poincare-type inequality by K. Oleszkiewicz Fractional sums and integrals of $r$-concave tails and applications to comparison probability inequalities by I. Pinelis Product formula, tails and independence of multiple stable integrals by J. Rosinski and G. Samorodnitsky A domination inequality for martingale polynomials by J. Szulga A log-concavity proof for a Gaussian exponential bound by R. A. Vitale.