LOCAL INVARIANCE PRINCIPLE FOR MARKOV CHAINS
Abstract: We consider stationary homogeneous Markov chains and the polygonal processes
defined by a usual way using such chains. There are many results about invariance
principles of those processes. In this paper, we prove that under additional conditions, a
stronger assertion (in some sense) is true. Indeed, we establish the convergence in
variation for the distributions of the functionals of such a process, that is a local
invariance principle. We study also the particular case of positive Harris recurrent
Markov chains. Finally, we prove that the invariance principle and the local invariance
principle remain valid when the initial chain is homogeneous but not stationary.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -