Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.163FAEPEX [1324/12]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAEPEX [1324/12]FAPESP [2012/18789-0]