This paper deals with the convergence in distribution to Gaussian, generalized Poisson and infinitely divisible laws of the row sums of certain $\phi$ or $\psi$-mixing triangular arrays of Banach space valued random vectors with stationary rows. Necessary and sufficient conditions for convergence in terms of individual r.v.'s are proved. These include sufficient conditions for the convergence to a stable law of the normalized sums of certain $\phi$-mixing, stationary sequences. An invariance principle for stationary, $\phi$-mixing triangular arrays is given.
Publié le : 1984-05-14
Classification:
Mixing triangular array,
Banach space valued random vector,
weak convergence of measures,
Gaussian measure,
$\tau$-centered Poisson measure,
infinitely divisible measure,
invariance principle,
60F05,
60B12,
60F17
@article{1176993297,
author = {Samur, Jorge D.},
title = {Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 390-426},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993297}
}
Samur, Jorge D. Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows. Ann. Probab., Tome 12 (1984) no. 4, pp. 390-426. http://gdmltest.u-ga.fr/item/1176993297/