  The paper studies a class of Ornstein-Uhlenbeck processes on the classical
Wiener space. These processes are associated with a diffusion type Dirichlet
form whose corresponding diffusion operator is unbounded in the Cameron-Martin
space. It is shown that the distributions of certain finite dimensional
Ornstein-Uhlenbeck processes converge weakly to the distribution of such an
infinite dimensional Ornstein-Uhlenbeck process. For the infinite dimensional
processes, the ordinary scalar quadratic variation is calculated. Moreover,
relative to the stochastic calculus via regularization, the scalar as well as
the tensor quadratic variation are derived. A related It\^o formula is
presented.
