Finite-memory elephant random walk and the central limit theorem for additive functionals

The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well-known result with long history. In this paper, we present applications to two finite-memory versions the Elephant Random Walk, solving problem from Gut and Stadtmüeller (2018). We also derivation CLT finite state chains, which based on positive recurrence, IID sequences some elementary linear algebra, focuses characterization variance.