Geodesic
On the negative dependence in Hilbert spaces with applications
Applications of Mathematics, Tome 64 (2019) no. 1, pp. 45-59.

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This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.
DOI : 10.21136/AM.2018.0060-18
Classification : 60B11, 60B12, 60F15
Keywords: negative dependence; pairwise negative dependence; Hilbert space; law of large numbers 
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Hien, Nguyen Thi Thanh; Thanh, Le Van; Van, Vo Thi Hong. On the negative dependence in Hilbert spaces with applications. Applications of Mathematics, Tome 64 (2019) no. 1, pp. 45-59. doi : 10.21136/AM.2018.0060-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0060-18/

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