Stochastic integral for non-adapted processes with respect to the Rosenblatt process

Abstract In this paper, we define the stochastic integral of an anticipating integrand (which is a product of instantly independent process and adapted process) with respect to the Rosenblatt process. The method is based on Ayed and Kuo’s approach [W. Ayed and H.-H. Kuo, An extension of the Itô integral, Commun. Stoch. Anal. 2 2008, 3, 323–333]. This will leads to model dynamics which driven by the Rosenblatt process with less information.