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Advances in Stochastic Inequalities
Edited by: Theodore P. Hill and Christian Houdré, Georgia Institute of Technology, Atlanta, GA

Contemporary Mathematics
1999; 212 pp; softcover
Volume: 234
ISBN-10: 0-8218-1086-3
ISBN-13: 978-0-8218-1086-6
List Price: US$51
Member Price: US$40.80
Order Code: CONM/234
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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.


Graduate students and research mathematicians working in probability and statistics; statisticians, economists, physicists, and engineers.

Table of Contents

  • P. C. Allaart -- Bounds on the non-convexity 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. Montgomery-Smith -- 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 Bonferroni-type inequality
  • R. P. Kertz -- Pricing-differentials 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 Poincaré-type 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 log-concavity proof for a Gaussian exponential bound
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