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Paper's Title:

Maximal Inequalities for Multidimensionally Indexed Demimartingales and the Hájek-Rényi Inequality for Associated Random Variables


Tasos C. Christofides and Milto Hadjikyriakou

Department of Mathematics and Statistics
University of Cyprus
P.O.Box 20537, Nicosia 1678, Cyprus


Demimartingales and demisubmartingales introduced by Newman and
Wright (1982) generalize the notion of martingales and
submartingales respectively. In this paper we define
multidimensionally indexed demimartingales and demisubmartingales
and prove a maximal inequality for this general class of random
variables. As a corollary we obtain a Hájek-Rényi inequality
for multidimensionally indexed associated random variables, the bound of which, when reduced to the case of single index, is sharper than the bounds already known in the literature.

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