The statistical literature abounds with limit results (central limit theorems, laws of large numbers and laws of iterated logarithm) for Markov chains, Markov renewal processes, and Markov additive processes. However, most of the general results are not applicable in practice because the limiting quantitites are not available in an explicit form, in general.
In the present lecture we will discuss a general and unifying approach for solving the above problem. This is based on viewing the above mentioned processes as exponential families. As such they exhibit some very nice properties which lead to explicit solutions in the functional and nonfunctional limit theory.