On the Abstract Subordinated Exit Equation
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...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/390218 |
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| author | Hassen Mejri Ezzedine Mliki |
| author_facet | Hassen Mejri Ezzedine Mliki |
| author_sort | Hassen Mejri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-84444605eeba4f7aa4704a1fd789d162 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-84444605eeba4f7aa4704a1fd789d1622025-02-03T07:25:20ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/390218390218On the Abstract Subordinated Exit EquationHassen Mejri0Ezzedine Mliki1Institut Supérieur d'Informatique et des Technologie de Communication de Hammam Sousse, 4011-G.P.1 Sousse, TunisiaInstitut Préparatoire aux Études d'Ingénieurs de Monastir, 5000 Monastir, TunisiaLet 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.http://dx.doi.org/10.1155/2010/390218 |
| spellingShingle | Hassen Mejri Ezzedine Mliki On the Abstract Subordinated Exit Equation Abstract and Applied Analysis |
| title | On the Abstract Subordinated Exit Equation |
| title_full | On the Abstract Subordinated Exit Equation |
| title_fullStr | On the Abstract Subordinated Exit Equation |
| title_full_unstemmed | On the Abstract Subordinated Exit Equation |
| title_short | On the Abstract Subordinated Exit Equation |
| title_sort | on the abstract subordinated exit equation |
| url | http://dx.doi.org/10.1155/2010/390218 |
| work_keys_str_mv | AT hassenmejri ontheabstractsubordinatedexitequation AT ezzedinemliki ontheabstractsubordinatedexitequation |