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On the Abstract Subordinated Exit Equation

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  • Hassen Mejri
  • Ezzedine Mliki

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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Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:390218
DOI: 10.1155/2010/390218
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