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June 2011 Processes with block-associated increments
Adam Jakubowski, Joanna Karłowska-Pik
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J. Appl. Probab. 48(2): 514-526 (June 2011). DOI: 10.1239/jap/1308662641


This paper is motivated by relations between association and independence of random variables. It is well known that, for real random variables, independence implies association in the sense of Esary, Proschan and Walkup (1967), while, for random vectors, this simple relationship breaks. We modify the notion of association in such a way that any vector-valued process with independent increments also has associated increments in the new sense - association between blocks. The new notion is quite natural and admits nice characterization for some classes of processes. In particular, using the covariance interpolation formula due to Houdré, Pérez-Abreu and Surgailis (1998), we show that within the class of multidimensional Gaussian processes, block association of increments is equivalent to supermodularity (in time) of the covariance functions. We also define corresponding versions of weak association, positive association, and negative association. It turns out that the central limit theorem for weakly associated random vectors due to Burton, Dabrowski and Dehling (1986) remains valid, if the weak association is relaxed to the weak association between blocks.


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Adam Jakubowski. Joanna Karłowska-Pik. "Processes with block-associated increments." J. Appl. Probab. 48 (2) 514 - 526, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1235.60056
MathSciNet: MR2840313
Digital Object Identifier: 10.1239/jap/1308662641

Primary: 60G99
Secondary: 60E07 , 60F05 , 60G15

Keywords: associated increments , association , independence , Independent increments , supermodularity , weak association

Rights: Copyright © 2011 Applied Probability Trust


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Vol.48 • No. 2 • June 2011
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