Wiener Functionals of Second Order and Their Lévy Measures
Hiroyuki Matsumoto, Nagoya University
Setsuo Taniguchi, Kyushu University
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.
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