Interpolation, correlation identities, and inequalities for infinitely divisible variables

We present an interpolation formula for the expectation of functions of infinitely divisible (i.d.) variables. This is then applied to study the association problem for i.d. vectors and to present new covariance expansions and correlation inequalities.

[1]  Béla Martos,et al.  Subdefinite Matrices and Quadratic Forms , 1969 .

[2]  L. Pitt.  A Gaussian Correlation Inequality for Symmetric Convex Sets , 1977 .

[3]  J. Glimm,et al.  Quantum Physics: A Functional Integral Point of View , 1981 .

[4]  L. Pitt.  Positively Correlated Normal Variables are Associated , 1982 .

[5]  Jacques A. Ferland,et al.  Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons , 1982, Math. Program..

[6]  米谷 民明,et al.  J. Glimm and A. Jaffe: Quantum Physics; A Functional Integral Point of View, Springer-Verlag, New York and Heidelberg, 1981, xx+418ページ, 24.5×16.5cm, DM62. , 1983 .

[7]  Louis H. Y. Chen.  Poincaré-type inequalities via stochastic integrals , 1985 .

[8]  Werner Linde,et al.  Probability in Banach Spaces: Stable and Infinitely Divisible Distributions , 1986 .

[9]  Louis H. Y. Chen.  Characterization of probability distributions by Poincaré-type inequalities , 1987 .

[10]  Sidney I. Resnick.  ASSOCIATION AND MULTIVARIATE EXTREME VALUE DISTRIBUTIONS , 1988 .

[11]  R. A. Vitale.  A differential version of the Efron-Stein inequality: bounding the variance of a function of an infinitely divisible variable , 1988 .

[12]  Gennady Samorodnitsky,et al.  Association of stable random variables , 1990 .

[13]  M. Ledoux.  L'algèbre de Lie des gradients itérés d'un générateur markovien , 1993 .

[14]  Gennady Samorodnitsky.  Association of Infinitely Divisible Random Vectors , 1995 .

[15]  Inequalities of correlation type for symmetric stable random vectors , 1995, math/9503212.

[16]  M. Lifshits.  Gaussian Random Functions , 1995 .

[17]  C. Houdré,et al.  Covariance Identities and Inequalities for Functionals on Wiener and Poisson Spaces , 1995 .

[18]  A. Kagan,et al.  Variance inequalities for functions of Gaussian variables , 1995 .

[19]  Vladimir I. Piterbarg,et al.  Asymptotic Methods in the Theory of Gaussian Processes and Fields , 1995 .

[20]  On the Gaussian measure of the intersection of symmetric, convex sets , 1996, math/9607210.

[21]  Yaozhong Hu,et al.  Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities , 1997 .

[22]  Gideon Schechtman,et al.  ON THE GAUSSIAN MEASURE OF THE INTERSECTION , 1998 .