Let be a -contraction semigroup on a real Banach space . A -exit law is a -valued function satisfying the functional equation: , . Let be a Bochner subordinator and let be the subordinated semigroup of (in the Bochner sense) by means of . Under some regularity assumption, it is proved in this paper that each -exit law is subordinated to a unique -exit law.
Hassen Mejri. Ezzedine Mliki. "On the Abstract Subordinated Exit Equation." Abstr. Appl. Anal. 2010 1 - 16, 2010. https://doi.org/10.1155/2010/390218