Weak invariance principle for the local times of partial sums of Markov Chains

Michael Bromberg, Zemer Kosloff

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 nor…