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 language | English (US) |
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Pages (from-to) | 361-371 |
Number of pages | 11 |
Journal | Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete |
Volume | 59 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1982 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- General Mathematics