Mark
Podolski
Universität Luxemburg
Recent advances in drift estimation for high-dimensional diffusion models
Abstract.
In this talk, we will present a selection of recent theoretical results on high-dimensional inference for the drift component of diffusion models. Such models have found numerous applications in areas including mathematical finance and biology among others. The primary focus will be on drift estimation for high-dimensional Ornstein-Uhlenbeck processes, although we will also discuss extensions to more general linear and nonlinear diffusion models. In particular, we will present Lasso-type estimators for sparse drift matrices, establish their statistical guarantees, and discuss consistent support recovery property. In the second part of the talk, we will consider drift estimation under low-rank constraints, a framework closely related to the concept of cointegration in continuous time. The presentation is based on joint work with Gabriela Ciołek, Dmytro Marushkevych, and Francisco Pina.