On the Abstract Subordinated Exit Equation

Abstract EN

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.