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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 16, Fasc. 2,
pages 185 - 199
 

A FUNCTIONAL CENTRAL LIMIT THEOREM UNDER UNIFORM MIXING ON A LOCALLY COMPACT ABELIAN GROUP

Michael S. Bingham

Abstract: A central limit theorem and a corresponding functional central limit theorem are given under a uniform mixing condition for uniformly infinitesimal triangular arrays of random variables which take values in a locally compact second countable Abelian group. The limiting distribution in the central limit theorem is Gaussian and the limiting distribution in the functional central limit theorem is the distribution of a Gaussian process with independent increments and continuous sample paths - a Wiener-type process.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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