  The purpose of these notes is to clarify the duality between a natural class
of jump processes on compact ultrametric spaces - studied in current work of
Bendikov, Girgor'yan and Pittet - and nearest neighbour walks on trees.
Processes of this type have appeared in recent work of Kigami. Every compact
ultrametric space arises as the boundary of a locally finite tree. The duality
arises via the Dirichlet forms: one on the tree associated with a random walk
and the other on the boundary of the tree, which is given in terms of the
Na\"im kernel. Here, it is explained that up to a linear time change by a
unique constant, there is a one-to-one correspondence between the above
processes and Dirichlet regular random walks.
