Limit theorems for singular Skorohod integrals

Abstract

In this paper we prove the convergence in distribution of sequences of Itô 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.