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Advances in Stochastic Inequalities
 
Edited by: Theodore P. Hill Georgia Institute of Technology, Atlanta, GA
Christian Houdré Georgia Institute of Technology, Atlanta, GA
Advances in Stochastic Inequalities
Softcover ISBN:  978-0-8218-1086-6
Product Code:  CONM/234
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7825-5
Product Code:  CONM/234.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1086-6
eBook: ISBN:  978-0-8218-7825-5
Product Code:  CONM/234.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Advances in Stochastic Inequalities
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Advances in Stochastic Inequalities
Edited by: Theodore P. Hill Georgia Institute of Technology, Atlanta, GA
Christian Houdré Georgia Institute of Technology, Atlanta, GA
Softcover ISBN:  978-0-8218-1086-6
Product Code:  CONM/234
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7825-5
Product Code:  CONM/234.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1086-6
eBook ISBN:  978-0-8218-7825-5
Product Code:  CONM/234.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2341999; 212 pp
    MSC: Primary 60; Secondary 62;

    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.

    Readership

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

  • Table of Contents
     
     
    • Articles
    • Pieter C. Allaart — Bounds on the non-convexity of ranges of vector measures with atoms [ MR 1694759 ]
    • Miguel A. Arcones — The class of Gaussian chaos of order two is closed by taking limits in distribution [ MR 1694760 ]
    • Richard C. Bradley — Two inequalities and some applications in connection with $\rho ^\ast $-mixing, a survey [ MR 1694761 ]
    • Wan-Ying Chang and Donald St. P. Richards — Variance inequalities for functions of multivariate random variables [ MR 1694762 ]
    • Paweł Hitczenko and Stephen Montgomery-Smith — A note on sums of independent random variables [ MR 1694763 ]
    • Yaozhong Hu — Exponential integrability of diffusion processes [ MR 1694764 ]
    • Adam Jakubowski and Jan Rosiński — Local dependencies in random fields via a Bonferroni-type inequality [ MR 1694765 ]
    • Robert P. Kertz — Pricing-differentials and bounds for lookback options, and prophet problems in probability [ MR 1694766 ]
    • Alexander Koldobsky — A correlation inequality for stable random vectors [ MR 1694767 ]
    • Rafał Latała — A note on the maximal inequalities for VC classes [ MR 1694768 ]
    • Krzysztof Oleszkiewicz — Comparison of moments via Poincaré-type inequality [ MR 1694769 ]
    • Iosif Pinelis — Fractional sums and integrals of $r$-concave tails and applications to comparison probability inequalities [ MR 1694770 ]
    • J. Rosiński and G. Samorodnitsky — Product formula, tails and independence of multiple stable integrals [ MR 1694771 ]
    • Jerzy Szulga — A domination inequality for martingale polynomials [ MR 1694772 ]
    • Richard A. Vitale — A log-concavity proof for a Gaussian exponential bound [ MR 1694773 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2341999; 212 pp
MSC: Primary 60; Secondary 62;

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.

Readership

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

  • Articles
  • Pieter C. Allaart — Bounds on the non-convexity of ranges of vector measures with atoms [ MR 1694759 ]
  • Miguel A. Arcones — The class of Gaussian chaos of order two is closed by taking limits in distribution [ MR 1694760 ]
  • Richard C. Bradley — Two inequalities and some applications in connection with $\rho ^\ast $-mixing, a survey [ MR 1694761 ]
  • Wan-Ying Chang and Donald St. P. Richards — Variance inequalities for functions of multivariate random variables [ MR 1694762 ]
  • Paweł Hitczenko and Stephen Montgomery-Smith — A note on sums of independent random variables [ MR 1694763 ]
  • Yaozhong Hu — Exponential integrability of diffusion processes [ MR 1694764 ]
  • Adam Jakubowski and Jan Rosiński — Local dependencies in random fields via a Bonferroni-type inequality [ MR 1694765 ]
  • Robert P. Kertz — Pricing-differentials and bounds for lookback options, and prophet problems in probability [ MR 1694766 ]
  • Alexander Koldobsky — A correlation inequality for stable random vectors [ MR 1694767 ]
  • Rafał Latała — A note on the maximal inequalities for VC classes [ MR 1694768 ]
  • Krzysztof Oleszkiewicz — Comparison of moments via Poincaré-type inequality [ MR 1694769 ]
  • Iosif Pinelis — Fractional sums and integrals of $r$-concave tails and applications to comparison probability inequalities [ MR 1694770 ]
  • J. Rosiński and G. Samorodnitsky — Product formula, tails and independence of multiple stable integrals [ MR 1694771 ]
  • Jerzy Szulga — A domination inequality for martingale polynomials [ MR 1694772 ]
  • Richard A. Vitale — A log-concavity proof for a Gaussian exponential bound [ MR 1694773 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.