Stable semigroups on homogeneous trees and hyperbolic spaces

Andrzej Stos (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We 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.

Mots clés: homogeneous trees; hyperbolic spaces; stable processes; subordination; heat kernel; metric measure space

Domaines: Probabilités [math.PR]

Andrzej Stos. Stable semigroups on homogeneous trees and hyperbolic spaces. 2006. ⟨hal-00079001⟩