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May, 1984 Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows
Jorge D. Samur
Ann. Probab. 12(2): 390-426 (May, 1984). DOI: 10.1214/aop/1176993297


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.


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Jorge D. Samur. "Convergence of Sums of Mixing Triangular Arrays of Random Vectors with Stationary Rows." Ann. Probab. 12 (2) 390 - 426, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

MathSciNet: MR735845
zbMATH: 0542.60012
Digital Object Identifier: 10.1214/aop/1176993297

Primary: 60F05
Secondary: 60B12 , 60F17

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

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 2 • May, 1984
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