  Let X_{n} be an integer valued Markov Chain with finite state space. Let
S_{n}=\sum_{k=0}^{n}X_{k} and let L_{n}(x) be the number of times S_{k} hits x
up to step n. Define the normalized local time process t_{n}(x) by
t_{n}(x)=\frac{L_{n}(\sqrt{n}(x)}{\sqrt{n}}. The subject of this paper is to
prove a functional, weak invariance principle for the normalized sequence
t_{n}, i.e. we prove that under some assumptions about the Markov Chain, the
normalized local times converge in distribution to the local time of the
Brownian Motion.
