## Abstract

We have already introduced the concept of a demimartingale extending the notion of a martingale and studied some of its properties. The class of demimartingales contains the sequences of partial sums of mean zero associated random variables as a special case. Motivated by the theory of demimartingales developed in Chapter 2, we now define (cf. Prakasa Rao (2002a) and Christofides (2003)) the class of *N*-demimartingales. We will see later that the sequence of partial sums of mean zero negatively associated (NA) random variables form an *N*-demimartingale. Throughout this chapter, we assume that the expectations of random variables under consideration exist.

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© Springer Basel AG 2012