Stationary and self-similar processes driven by Lévy processes (Q1613667)

The paper presents a construction of a (strictly) stationary process with prescribed one-dimensional law. The law is provided of type G, i.e. the law of a product \(\sigma W\) where \(W\) is a random vector with standard normal distribution and \(\sigma >0\) is a random variable independent with \(W\). The construction is based on integration along a bivariate Lévy process. Using classical transformation, due to Lamperti (1962), \(H\)-self-similar processes are derived and discussed for \(H\in (0,{1\over 2})\cup ({1\over 2},1)\).