Abstract
Let P = (P-t)(t>0) be a C-0-contraction semigroup on a real Banach space B. A P-exit law is a B-valued function t is an element of]0,infinity[-> phi(t) is an element of B satisfying the functional equation: P-t phi(s) = phi(t+s), s, t > 0. Let beta be a Bochner subordinator and let P-beta be the subordinated semigroup of P (in the Bochner sense) by means of beta. Under some regularity assumption, it is proved in this paper that each P-beta-exit law is subordinated to a unique P-exit law.