On the abstract subordinated exit equation
type: Item
instance of: scholarly article
title: On the abstract subordinated exit equation
zbMATH Open document ID: 1223.47040
DOI: 10.1155/2010/390218
author: Hassen Mejri
author: Ezzedine Mliki
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/227335
review text: Summary: Let \(\mathbb P=(P_t)_{t>0}\) be a \(C_0\)-contraction semigroup on a real Banach space \(\mathcal B\). A \(\mathbb P\)-exit law is a \(\mathcal B\)-valued function \(t \in ]0,\infty[\to \varphi_t \in \mathcal B\) satisfying the functional equation \(P_t\varphi_s=\varphi_{t+s}\), \(s, t > 0\). Let \(\beta\) be a Bochner subordinator and let \(\mathbb P^\beta\) be the subordinated semigroup of \(\mathbb P\) (in the Bochner sense) by means of \(\beta\). Under some regularity assumptions, it is proved in this paper that each \(\mathbb P^\beta\)-exit law is subordinated to a unique \(\mathbb P\)-exit law.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N30
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 5791618
Wikidata QID: Q58649838
MaRDI profile type: Publication
OpenAlex ID: W1968154708
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description: scientific article; zbMATH DE number 5791618