Weak convergence of functionals of stationary processes to Rosenblatt-type distributions

We provide an asymptotic result for the distribution of functionals of continuous Gaussian processes with long memory. Much of the existing literature on the subject resorts to asymptotic representations based on stochastic integrals. However, the method of proof used here, based on characteristic functions, enables one to extend the class of functionals for which we are able to provide an asymptotic representation. Next, we study the properties of the asymptotic process and finally, as an application, we consider the case of continuous regression where the process of errors follows a Gamma process with long-range dependence.