On the local limit theorems for lower psi-mixing Markov chains

Florence Merlevède, Magda Peligrad, Costel Peligrad

Published 2021-10-19, updated 2022-05-29Version 2

In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases. The results are also new in the stationary setting and lead to local limit theorems linked to convergence to stable distributions. The conditions are imposed to individual summands and are expressed in terms of lower psi-mixing coefficients.