Limit theorems for singular Skorohod integrals

In this paper we prove the convergence in distribution of sequences of It^o and Skorohod integrals with integrands having singular asymptotic behavior. These sequences include stochastic convolutions and generalize the example $\sqrt{n}{\int }_0^1{t}^n{B}_{t}d{B}_t$ first studied by Peccati and Yor in 2004.