ADAPTED TRANSFORMATIONS OF ORDER ONE AND QUADRATIC FORMS ON WIENER SPACES

抄録

It will be shown that every adapted transformation of order one on a Wiener space gives rise to an exponentially integrable quadratic form through a change-of-variables formula, and conversely each exponentially integrable quadratic form has an adapted transformation of order one realizing the form in such a manner. This bidirectional relationship is applied to adapted linear transformations to see the equivalence between the exponential integrability of quadratic forms and the solvability of the Riccati equation. Furthermore, thanks to this equivalence, an explicit representation of the Feynman–Kac density function will be achieved.