2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142131We consider a time-homogeneous Markov chain $X_n$, $n\ge0$, valued in ${\bf R}$. Suppose that this chain is transient, that is, $X_n$ generates a $σ$-finite renewal measure. We prove the key renewal theorem under condition that this chain has asymptotically homogeneous at infinity jumps and asymptotically positive drift.12 pagesProbability60K05text