Abstract: Given a Markov chainwith finite state space and irreducible primitive stationary transition matrix
, at time
, corresponding to each possible one-step transition
, we associate random variables
with distribution
depending only on states
and/or
. Given
,
,
are conditionally independent and need not be integer-valued, nor positive. Define the cumulative sum
with
It is proved under certain conditions that the limiting distribution of
is in the class of compound Poisson type distributions. Some applications of the theorem are illustrated.
Key words and phrases: Compound Poisson distribution, convergence theorem, interarrival time, limiting distribution, Markov chain, Markov renewal process, sum of random variables.