ON THE CONVERGENCE OF WEIGHTED AVERAGES OF RANDOM
VARIABLES ARISING FROM A FINITE MARKOV CHAIN
Abstract: Jamison et al. [6] discussed the convergence of weighted sums of independent
random variables to a degenerate random variable. In this note one of their results is
extended (with the same condition on the weights) to the sequence of holding times of
a Markov Renewal process. A similar growth condition on the weights ensures
the convergence of these weighted sums (suitably normalized) to the Normal law.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -