A white noise approach to infinitely divisible distributions on Gel'fand triple

摘要

In this note, we apply white noise analysis to infinitely divisible distributions on a real Gel'fand triple E subset of H subset of E*. We first introduce an index, called Hida index, for a measure on E subset of H subset of 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 subset of H subset of E* and that of its Levy measure. Finally we prove that the Hida index of the standard compound Poisson distribution on E subset of H subset of E* is exactly 1. (c) 2005 Elsevier Inc. All rights reserved.