Abstract and Applied Analysis
Volume 2010 (2010), Article ID 390218, 16 pages
doi:10.1155/2010/390218
Review Article

On the Abstract Subordinated Exit Equation

Hassen Mejri1 and Ezzedine Mliki2

1Institut Supérieur d'Informatique et des Technologie de Communication de Hammam Sousse, 4011-G.P.1 Sousse, Tunisia
2Institut Préparatoire aux Études d'Ingénieurs de Monastir, 5000 Monastir, Tunisia

Received 7 March 2010; Revised 10 May 2010; Accepted 11 May 2010

Academic Editor: Nikolaos Papageorgiou

Copyright © 2010 Hassen Mejri and Ezzedine Mliki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.