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