I am a doctoral student at the KIT Institute for Applied and Numerical Mathematics and my research primarily focuses on the development of statistical methods for the robust estimation of effective models, that are described by a stochastic differential equation (SDE), under observations which essentially come from a model that is a “weakly perturbed version” of the effective model. To be more precise, this weakly perturbed version is a multiscale SDE system with respect to time, depending on a small time-scale parameter, and the effective model is a homogenized SDE that emerges in the (weak) limit when the time-scale parameter goes to zero. In recent times it has been rigorously shown that standard statistical learning methodologies, e.g. maximum likelihood estimation, fail to provide consistent estimates for homogenized SDEs when the estimation method is confronted with multiscale observations, i.e. data that is not coming from the true effective model. This is a peculiarity since the data is coming from a model that is still very close to the effective model, at least in a weak sense. Despite this being a rather non-classical framework for the statistical inference, it is virtually quite important for applications as there is almost always a discrepancy between the "true" model, chosen by the statistician, and the model that actually generated the observations.

At the moment, I am specifically working on the statistical properties of a minimum distance estimator in a parametric setting and substantiating the theoretical findings through numerical evidence in several case studies.

This research project is fully funded by the SFB 1481, Sparsity and Singular Structures.