A Probabilistic Inequality Related to Negative Definite Functions

Research output: Contribution to book/Conference proceedings/Anthology/Report › Chapter in book/Anthology/Report › Contributed › peer-review

Contributors

  • Mikhail Lifshits - , St. Petersburg State University (Author)
  • René L. Schilling - , Chair of Probability Theory (Author)
  • Ilya Tyurin - , Lomonosov Moscow State University (Author)

Abstract

We prove that for any pair of i.i.d. random vectors X,Y in (formula presented) and any real-valued continuous negative definite function (formula presented) the inequality(formula presented) holds. In particular, for (formula presented) and the Euclidean norm (formula presented) one has (formula presented) The latter inequality is due to A. Buja et al. [4] where it is used for some applications in multivariate statistics. We show a surprising connection with bifractional Brownian motion and provide some related counter-examples.

Details

Original languageEnglish
Title of host publicationHigh Dimensional Probability VI. The Banff Volume.
PublisherBirkhauser Verlag Basel
Pages73-80
Number of pages8
Publication statusPublished - 2013
Peer-reviewedYes

Publication series

SeriesProgress in probability : PP
Volume66
ISSN1050-6977

Keywords

ASJC Scopus subject areas

Keywords

  • Bernstein functions, Bifractional Brownian motion, moment inequalities, negative definite functions