A setting of the change-point estimation problem with a “smooth” change is investigated. A special class of such models, where the change is defined as a gradual shift in the parameter, is considered. We show that these models can be analyzed via explicitly given procedures. It is demonstrated that M -estimators can consistently estimate the change in the parameter structure as well as the addi...

We consider the dyadic model, which is a toy model to test issues of wellposedness and blow-up for the Navier–Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier–Stokes. Likewise we prove wellposedness for the inviscid problem (in a suitable regularity class) when the parameter corresponds to ...