Abstract. In this paper, infinite-dimensional
Ito processes with respect to a symmetric Gaussian random measure Z taking values in a Banach space
are defined. Under some assumptions, it is shown that if Xt is an Ito process with
respect to Z and g(t, x) is a C2-smooth mapping then Yt = g(t, Xt) is again an Ito
process with respect to Z. A
general infinite-dimensional Ito formula is established.