Abstract. In this paper, infinitedimensional
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 X_{t} is an Ito process with
respect to Z and g(t, x) is a C^{2}smooth mapping then Y_{t} = g(t, X_{t}) is again an Ito
process with respect to Z. A
general infinitedimensional Ito formula is established.
