Article ID Journal Published Year Pages File Type
4624037 Journal of Mathematical Analysis and Applications 2006 11 Pages PDF
Abstract

In this note, we apply white noise analysis to infinitely divisible distributions on a real Gel'fand triple E⊂H⊂E∗. We first introduce an index, called Hida index, for a measure on E⊂H⊂E∗. And then, under some mild conditions, we obtain a general inequality which indicates a connection between the Hida index of an infinitely divisible distribution on E⊂H⊂E∗ and that of its Lévy measure. Finally we prove that the Hida index of the standard compound Poisson distribution on E⊂H⊂E∗ is exactly 1.

Related Topics
Physical Sciences and Engineering Mathematics Analysis