## The Annals of Probability

### Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows

Jorge D. Samur

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 12, Number 2 (1984), 390-426.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993297

Digital Object Identifier
doi:10.1214/aop/1176993297

Mathematical Reviews number (MathSciNet)
MR735845

Zentralblatt MATH identifier
0542.60012

JSTOR