We study the existence and uniqueness of the solution for a one-dimensional
anticipative stochastic evolution equation driven by a two-parameter Wiene
r process W-t,W-x and based on a stochastic semigroup p (s, t, y, x). The k
ernel p(s, t, y, x) is supposed to be measurable with respect to the increm
ents of the Wiener process on [s, t] x R. The results are based on L-p-esti
mates for the Skorohod integral. As a application we deduce the existence o
f a weak solution for the stochastic partial differential equation
partial derivative u/partial derivative t = partial derivative(2)u/partial
derivative x(2) + (v) over dot(t, x) partial derivative u/partial derivativ
e x + F(t, x, u) partial derivative(2)W/partial derivative t partial deriva
tive x,
where (v) over dot(t, x) is a white-noise in time. (C) 2000 Editions scient
ifiques et medicales Elsevier SAS.