Stochastic integration with respect to the cylindrical Wiener process   via regularization
  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 Winer 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. 
Christian Olivera
math.FA math.PR