On the negative dependence in Hilbert spaces with applications

Nguyen Thi Thanh Hien; Le Van Thanh; Vo Thi Hong Van

Applications of Mathematics (2019)

  • Volume: 64, Issue: 1, page 45-59
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hien, Nguyen Thi Thanh, Thanh, Le Van, and Van, Vo Thi Hong. "On the negative dependence in Hilbert spaces with applications." Applications of Mathematics 64.1 (2019): 45-59. <http://eudml.org/doc/294534>.

@article{Hien2019,
abstract = {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.},
author = {Hien, Nguyen Thi Thanh, Thanh, Le Van, Van, Vo Thi Hong},
journal = {Applications of Mathematics},
keywords = {negative dependence; pairwise negative dependence; Hilbert space; law of large numbers},
language = {eng},
number = {1},
pages = {45-59},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the negative dependence in Hilbert spaces with applications},
url = {http://eudml.org/doc/294534},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Hien, Nguyen Thi Thanh
AU - Thanh, Le Van
AU - Van, Vo Thi Hong
TI - On the negative dependence in Hilbert spaces with applications
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 45
EP - 59
AB - 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.
LA - eng
KW - negative dependence; pairwise negative dependence; Hilbert space; law of large numbers
UR - http://eudml.org/doc/294534
ER -

References

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