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Titlebook: Associated Sequences, Demimartingales and Nonparametric Inference; B.L.S. Prakasa Rao Book 2012 Springer Basel AG 2012

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Multidimensionally Indexed Demimartingales and Continuous Parameter Demimartingales,stic processes with index in one-dimension. We now introduce more general demimartingales such as multidimensionally indexed demimartingales and continuous parameter demisubmartingales and discuss maximal inequalities for such processes.
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Associated Random Variables and Related Concepts,ever in some real life situations, the random variables need not be independent. In reliability studies, there are structures in which the components share the load, so that failure of one component results in increased load on each of the remaining components. Minimal path structures of a coherent
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,-Demimartingales,artingales 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 .-demimartingales. We will see later that the
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Limit Theorems for Associated Random Variables, 2 and some probabilistic properties of associated sequences in Chapter 1. Let . be a probability space and {..,.≥1} be a sequence of associated random vari- ables defined on it. Recall that a finite collection {..,..,…,..} is said to be associated if for every pair of functions .(.) and .(.) from .
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