The Annals of Probability

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

Jorge D. Samur

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case) 60F17: Functional limit theorems; invariance principles

Keywords
Mixing triangular array Banach space valued random vector weak convergence of measures Gaussian measure $\tau$-centered Poisson measure infinitely divisible measure invariance principle

Citation

Samur, Jorge D. Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows. Ann. Probab. 12 (1984), no. 2, 390--426. doi:10.1214/aop/1176993297. https://projecteuclid.org/euclid.aop/1176993297


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