Contemporary Mathematics 1999; 212 pp; softcover Volume: 234 ISBN10: 0821810863 ISBN13: 9780821810866 List Price: US$54 Member Price: US$43.20 Order Code: CONM/234
 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 stateoftheart 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; Bonferronitype inequalities for sums of stationary sequences; Rosenthaltype 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 meanzero Gaussian processes. Various articles in the book emphasize applications of stochastic inequalities to hypothesis testing, mathematical finance, statistics, and mathematical physics. Readership Graduate students and research mathematicians working in probability and statistics; statisticians, economists, physicists, and engineers. Table of Contents  P. C. Allaart  Bounds on the nonconvexity of ranges of vector measures with atoms
 M. A. Arcones  The class of Gaussian chaos of order two is closed by taking limits in distribution
 R. C. Bradley  Two inequalities and some applications in connection with \(\rho*\)mixing, a survey
 W.Y. Chang and D. St. P. Richards  Variance inequalities for functions of multivariate random variables
 P. Hitczenko and S. MontgomerySmith  A note on sums of independent random variables
 Y. Hu  Exponential integrability of diffusion processes
 A. Jakubowski and J. Rosiński  Local dependencies in random fields via a Bonferronitype inequality
 R. P. Kertz  Pricingdifferentials and bounds for lookback options, and prophet problems in probability
 A. Koldobsky  A correlation inequality for stable random vectors
 R. Latała  A note on the maximal inequalities for VC classes
 K. Oleszkiewicz  Comparison of moments via Poincarétype inequality
 I. Pinelis  Fractional sums and integrals of \(r\)concave tails and applications to comparison probability inequalities
 J. Rosiński and G. Samorodnitsky  Product formula, tails and independence of multiple stable integrals
 J. Szulga  A domination inequality for martingale polynomials
 R. A. Vitale  A logconcavity proof for a Gaussian exponential bound
