  Our aim is to find sufficient conditions for weak convergence of stochastic
integrals with respect to the state occupation measure of a Markov chain.
First, we study properties of the state indicator function and the state
occupation measure of a Markov chain. In particular, we establish weak
convergence of the state occupation measure under a scaling of the generator
matrix. Then, relying on the connection between the state occupation measure
and the Dynkin martingale related to the state indicator function, we provide
sufficient conditions for weak convergence of stochastic integrals with respect
to the state occupation measure.
