Associated random variables and martingale inequalities

C. M. Newman, A. L. Wright

Research output: Contribution to journalArticlepeer-review

Abstract

Many of the classical submartingale inequalities, including Doob's maximal inequality and upcrossing inequality, are valid for sequences Sj such that the (Sj+1-Sj's are associated (positive mean) random variables, and for more general "demisubmartingales". The demisubmartingale maximal inequality is used to prove weak convergence to the two-parameter Wiener process of the partial sum processes constructed from a stationary two-parameter sequence of associated random variables Xijwith {Mathematical expression}.

Original languageEnglish (US)
Pages (from-to)361-371
Number of pages11
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume59
Issue number3
DOIs
StatePublished - Sep 1982

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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