2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113813We prove the kernel estimates related to subordinated semigroups on homogeneous trees. We study the long time propagation problem. We exploit this to show exit time estimates for (large) balls. We use an abstract setting of metric measure spaces. This enables us to give these results for trees end hyperbolic spaces as well. Finally, we show some estimates for the Poisson kernel of a ball.ProbabilityPrimary 60J35; Secondary 47D03,14M17text