## Advances in Stochastic Inequalities: AMS Special Session on Stochastic Inequalities and Their Applications, October 17-19, 1997, Georgia Institute of TechnologyThis 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. |

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### Contents

1 | |

The class of Gaussian chaos of order two is closed by taking limits in distribution | 13 |

Two inequalities and some applications in connection with p mixing a survey | 21 |

Variance inequalities for functions of multivariate random variables | 43 |

A note on sums of independent random variables | 69 |

Exponential integrability of diffusion processes | 75 |

Local dependencies in random fields via a Bonferronitype inequality | 85 |

Pricingdifferentials and bounds for lookback options and prophet problems in probability | 97 |

A correlation inequality for stable random vectors | 121 |

A note on the maximal inequalities for VC classes | 125 |

Comparison of moments via Poincarétype inequality | 135 |

Fractional sums and integrals of rconcave tails and applications to comparison probability inequalities | 149 |

Product formula tails and independence of multiple stable integrals | 169 |

A domination inequality for martingale polynomials | 195 |

A logconcavity proof for a Gaussian exponential bound | 209 |

### Other editions - View all

Advances in Stochastic Inequalities: AMS Special Session on Stochastic ... Theodore Preston Hill,Christian Houdré No preview available - 1999 |

### Common terms and phrases

application assume assumption Banach space beta distribution bound call option central limit theorem chaos coefficients condition convergence convex Corollary defined denote dependence Dirichlet distributions eigenvalues equation example exists exponential integrability finite follows formula function f Gaussian given Hence Houdré implies independent random induction infinitely Jacobi polynomials Khinchine inequality Lemma Let X1 linear lookback option martingale Math Mathematics Subject Classification multiple integrals multivariate nonempty nonnegative norm obtain partition Peligrad Poisson probability processes proof of Theorem Proposition prove r-concave r—ro Rademacher random fields random measure random sequence random variables random vector REMARK result satisfies Section Shiryaev spectral density square-integrable statement stochastic stock-and-bond market strictly stationary sums Suppose supremum tail Theorem 3.1 theory values Varg(X1 variance inequalities VC class vector atom vector measure