Journal of Applied Probability
- J. Appl. Probab.
- Volume 48, Number 2 (2011), 514-526.
Processes with block-associated increments
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.
J. Appl. Probab., Volume 48, Number 2 (2011), 514-526.
First available in Project Euclid: 21 June 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G99: None of the above, but in this section
Secondary: 60G15: Gaussian processes 60E07: Infinitely divisible distributions; stable distributions 60F05: Central limit and other weak theorems
Jakubowski, Adam; Karłowska-Pik, Joanna. Processes with block-associated increments. J. Appl. Probab. 48 (2011), no. 2, 514--526. doi:10.1239/jap/1308662641. https://projecteuclid.org/euclid.jap/1308662641