CONDITIONED FUNCTIONAL CENTRAL LIMIT THEOREM FOR
RANDOM PARTIAL SUMS
Abstract: Generalization of a conditioned functional central limit theorem of Szubarga and
Szynal [6] is proved. It is shown that on a natural condition for random index randomly
selected partial sums of independent, identically distributed random variables with zero mean
and finite variance, suitably scaled, normed and conditioned to stay positive converge to the
Brownian meander process.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -