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Abstract: This paper is motivated by relations between association and independence ofrandom variables. It is well-known that for real random variables independenceimplies association in the sense of Esary, Proschan and Walkup, while forrandom vectors this simple relationship breaks. We modify the notion ofassociation in such a way that any vector-valued process with independentincrements has also associated increments in the new sense - associationbetween blocks. The new notion is quite natural and admits nicecharacterization for some classes of processes. In particular, using thecovariance interpolation formula due to Houdr\-{e}, P\-{e}rez-Abreu andSurgailis, we show that within the class of multidimensional Gaussian processesblock-association of increments is equivalent to supermodularity in time ofthe covariance functions. We define also corresponding versions of weakassociation, positive association and negative association. It turns out thatthe Central Limit Theorem for weakly associated random vectors due to Burton,Dabrowski and Dehling remains valid, if the weak association is relaxed to theweak association between blocks.

Author: Adam Jakubowski, Joanna Karlowska-Pik


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