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On the Abstract Subordinated Exit Equation

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  • Hassen Mejri
  • Ezzedine Mliki

Abstract

Let â„™ = ( 𠑃 ð ‘¡ ) ð ‘¡ > 0 be a ð ¶ 0 -contraction semigroup on a real Banach space ℬ . A â„™ - exit law is a ℬ -valued function ð ‘¡ ∈ ] 0 , ∞ [ → 𠜑 ð ‘¡ ∈ ℬ satisfying the functional equation: 𠑃 ð ‘¡ 𠜑 ð ‘ = 𠜑 ð ‘¡ + ð ‘ , ð ‘ , ð ‘¡ > 0 . Let ð ›½ be a Bochner subordinator and let â„™ ð ›½ be the subordinated semigroup of â„™ (in the Bochner sense) by means of ð ›½ . Under some regularity assumption, it is proved in this paper that each â„™ ð ›½ -exit law is subordinated to a unique â„™ -exit law.

Suggested Citation

  • Hassen Mejri & Ezzedine Mliki, 2010. "On the Abstract Subordinated Exit Equation," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-16, June.
    • Handle: RePEc:hin:jnlaaa:390218
    DOI: 10.1155/2010/390218
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