This article focuses on a new concept of quadratic variation for processes taking values in a Banach space B and a corresponding covariation. This is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace ? of the dual of the projective...

The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Hilbert space H, is the sum of a local...