Wiener Functionals of Second Order and Their Lévy Measures

Abstract

The distributions of Wiener functionals of second order are infinitely divisible. An explicit expression of the associated Lévy measures in terms of the eigenvalues of the corresponding Hilbert-Schmidt operators on the Cameron-Martin subspace is presented. In some special cases, a formula for the densities of the distributions is given. As an application of the explicit expression, an exponential decay property of the characteristic functions of the Wiener functionals is discussed. In three typical examples, complete descriptions are given.