2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173600An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the context of large deviations.12 pagesProbabilitySpectral Theory60F05, 60F10, 60J10, 47N30text