**Contemporary Mathematics**

Volume: 234;
1999;
212 pp;
Softcover

MSC: Primary 60;
Secondary 62

Print ISBN: 978-0-8218-1086-6

Product Code: CONM/234

List Price: $54.00

AMS Member Price: $43.20

MAA Member Price: $48.60

**Electronic ISBN: 978-0-8218-7825-5
Product Code: CONM/234.E**

List Price: $54.00

AMS Member Price: $43.20

MAA Member Price: $48.60

# Advances in Stochastic Inequalities

Share this page *Edited by *
*Theodore P. Hill; Christian Houdré*

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

## Advances in Stochastic Inequalities

- Contents vii8 free
- Preface ix10 free
- Bounds on the non-convexity of ranges of vector measures with atoms 112 free
- The class of Gaussian chaos of order two is closed by taking limits in distribution 1324
- Two inequalities and some applications in connection with p* -mixing, a survey 2132
- Variance inequalities for functions of multivariate random variables 4354
- A note on sums of independent random variables 6980
- Exponential integrability of diffusion processes 7586
- Local dependencies in random fields via a Bonferroni-type inequality 8596
- Pricing-differentials and bounds for lookback options, and prophet problems in probability 97108
- A correlation inequality for stable random vectors 121132
- A note on the maximal inequalities for VC classes 125136
- Comparison of moments via Poincaré-type inequality 135146
- Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities 149160
- Product formula, tails and independence of multiple stable integrals 169180
- A domination inequality for martingale polynomials 195206
- A log-concavity proof for a Gaussian exponential bound 209220