Some limit theorems for rescaled Wick powers
  We establish the strong L2(P)-convergence of properly rescaled Wick powers as the power index tends to infinity. The explicit representation of such limit will also provide the convergence in distribution to normal and log-normal random variables. The proofs rely on some estimates for the L2(P)-norm of Wick products and on the properties of second quantization operators. 
Alberto Lanconelli