Abstract
Let ℙ = (Pt) t>0 be a C0‐contraction semigroup on a real Banach space ℬ. A ℙ‐exit law is a ℬ‐valued function t∈]0, ∞[→φt ∈ ℬ satisfying the functional equation: Ptφs = φt+s, s, t > 0. Let β be a Bochner subordinator and let ℙβ be the subordinated semigroup of ℙ (in the Bochner sense) by means of β. Under some regularity assumption, it is proved in this paper that each ℙβ‐exit law is subordinated to a unique ℙ‐exit law.
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