  In this paper, we define a stochastic calculus with respect to the Rosenblatt
process by means of white noise distribution theory. For this purpose, we
compute the translated characteristic function of the Rosenblatt process at
time $t>0$ in any direction $\xi\in S(\mathbb{R})$ and the derivative of the
Rosenblatt process in the white noise sense. Using Wick multiplication by the
former derivative and Pettis integration, we define our stochastic integral
with respect to the Rosenblatt process for a wide class of distribution
processes. We obtain an explicit formula for the variance of such a stochastic
integral and It\^o's formulae for a certain class of functionals of the
Rosenblatt process. Finally, we compare our stochastic integral to other
approaches.
