A nonlinear Schrödinger equation with fractional noise

We study a stochastic Schrödinger equation with quadratic nonlinearity and space-time fractional perturbation, in space dimension d ≤ 3 d\leq 3 . When the Hurst index is large enough, we prove local well-posedness of problem using classical arguments. However, for small index, even interpretation needs some care. In this case, renormalization procedure must come into picture, leading to Wick-type model. Our fixed-point argument then involves specific regularization properties group, which allows us cope strong irregularity solution.