2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104908In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the particular case of transient Bessel processes, we note that this criterion agrees with the one obtained via Jeulin's convergence lemma.Probability60J65, 60J60text