This talk develops some aspects of stochastic calculus via regularization for processes with values in a general Banach space $B$. A new concept of quadratic variation which depends on a particular subspace is introduced. An It\^o formula and stability results for processes admitting this kind of quadratic variation are presented. Particular interest is devoted to the case when $B$ is the space of real continuous functions defined on $[-T,0]$, $T>0$ and the process is the window process $X(\cdot)$ associated with a continuous real process $X$ which, at time $t$, it takes into account the past of the process. If $X$ is a finite quadratic variation process (for instance Dirichlet, weak Dirichlet), it is possible to represent a large class of path-dependent random variable $h$ as a real number plus a real forward integral in a semiexplicite form. This representation result of $h$ makes use of a functional solving an infinite dimensional partial differential equation. This decomposition generalizes, in some cases, the Clark-Ocone formula which is true when $X$ is the standard Brownian motion $W$. Some stability results will be given explicitly.\\ This is a joint work with Francesco Russo (ENSTA ParisTech Paris)