  We consider the effective surface motion of a particle that intermittently
unbinds from a planar surface and performs bulk excursions. Based on a random
walk approach we derive the diffusion equations for surface and bulk diffusion
including the surface-bulk coupling. From these exact dynamic equations we
analytically obtain the propagator of the effective surface motion. This
approach allows us to deduce a superdiffusive, Cauchy-type behavior on the
surface, together with exact cutoffs limiting the Cauchy form. Moreover we
study the long-time dynamics for the surface motion.
