Journal of the
Korean Mathematical Society JKMS

In this note we reformulate the white noise calculus on the classical Wiener space $(\mathcal C',\mathcal C)$. It is shown that most of the examples and operators can be redefined on $\mathcal C$ without difficulties except the Hida derivative. To overcome the difficulty, we find that it is sufficient to replace $\mathcal C$ by $L_{_2}[0,1]$ and reformulate the white noise on the modified abstract Wiener space $({\mathcal C}',L_{_2}[0,1])$. The generalized white noise functionals are then defined and studied through their linear functional forms. For applications, we reprove the It{\^o} formula and give the existence theorem of one-side stochastic integrals with anticipating integrands.

Keywords: Wiener space, white noise, generalized functions

MSC numbers: 60G20, 60H99