Softcover ISBN:  9780821810866 
Product Code:  CONM/234 
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eBook ISBN:  9780821878255 
Product Code:  CONM/234.E 
List Price:  $125.00 
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AMS Member Price:  $100.00 
Softcover ISBN:  9780821810866 
eBook: ISBN:  9780821878255 
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 
Softcover ISBN:  9780821810866 
Product Code:  CONM/234 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821878255 
Product Code:  CONM/234.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821810866 
eBook ISBN:  9780821878255 
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 DetailsContemporary MathematicsVolume: 234; 1999; 212 ppMSC: 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 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.
ReadershipGraduate students and research mathematicians working in probability and statistics; statisticians, economists, physicists, and engineers.

Table of Contents

Articles

Pieter C. Allaart — Bounds on the nonconvexity 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 ]

WanYing Chang and Donald St. P. Richards — Variance inequalities for functions of multivariate random variables [ MR 1694762 ]

Paweł Hitczenko and Stephen MontgomerySmith — 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 Bonferronitype inequality [ MR 1694765 ]

Robert P. Kertz — Pricingdifferentials 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 Poincarétype 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 logconcavity proof for a Gaussian exponential bound [ MR 1694773 ]


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

Articles

Pieter C. Allaart — Bounds on the nonconvexity 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 ]

WanYing Chang and Donald St. P. Richards — Variance inequalities for functions of multivariate random variables [ MR 1694762 ]

Paweł Hitczenko and Stephen MontgomerySmith — 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 Bonferronitype inequality [ MR 1694765 ]

Robert P. Kertz — Pricingdifferentials 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 Poincarétype 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 logconcavity proof for a Gaussian exponential bound [ MR 1694773 ]