Open Access
August, 1976 Functional Central Limit Theorems in Banach Spaces
D. J. H. Garling
Ann. Probab. 4(4): 600-611 (August, 1976). DOI: 10.1214/aop/1176996030


Suppose that $(X_{nj})$ is a triangular array of random variables taking values in a Banach space $E$ and that $(B_n)$ is the corresponding sequence of random paths in $E$. Conditions are considered under which the distributions of $B_n$ converge to a Gaussian measure on $C(\lbrack 0, 1 \rbrack; E)$. Under stronger conditions on the array it is shown that if $E$ is of type 2 the paths enjoy certain regularity properties, which are reflected in the convergence. The technique here is to factorise the integration procedure by which one passes from the array to the sequence of paths, using fractional integrals.


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D. J. H. Garling. "Functional Central Limit Theorems in Banach Spaces." Ann. Probab. 4 (4) 600 - 611, August, 1976.


Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0343.60015
MathSciNet: MR423449
Digital Object Identifier: 10.1214/aop/1176996030

Primary: 60F05
Secondary: 28A40

Keywords: Banach spaces of type 2 , central limit theorems , triangular arrays

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 4 • August, 1976
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