Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624037 | Journal of Mathematical Analysis and Applications | 2006 | 11 Pages |
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.
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