Change-point tests under local alternatives for long-range dependent processes

We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cram\'er-von Mises type statistics are investigated. A special feature of distributional changes is the fact that the Hermite rank may change, too. We consider local alternatives covering this scenario, and as a result, we may derive the asymptotic power of the change point tests.