  We consider a $p$-Laplace evolution problem with stochastic forcing on a
bounded domain $D\subset\mathbb{R}^d$ with homogeneous Dirichlet boundary
conditions for $1<p<\infty$. The additive noise term is given by a stochastic
integral in the sense of It\^{o}. The technical difficulties arise from the
merely integrable random initial data $u_0$ under consideration. Due to the
poor regularity of the initial data, estimates in $W^{1,p}_0(D)$ are available
with respect to truncations of the solution only and therefore well-posedness
results have to be formulated in the sense of generalized solutions. We extend
the notion of renormalized solution for this type of SPDEs, show well-posedness
in this setting and study the Markov properties of solutions.
