Tatiana Orlova (University of Duisburg-Essen)

Spectral Bootstrap confidence bands for Lévy-driven moving average processes

This report will consider the problem of constructing bootstrap confidence intervals for the Lévy density of the driving Lévy process based on highfrequency observations of a Lévy-driven moving average processes. Using a spectral estimator of the Lévy density, we propose a novel implementations of multiplier  bootstraps to construct confidence bands on a compact set away from the origin. We also provide conditions under which the confidence bands are asymptotically valid.

Philipp Petersen (University of Vienna)
Approximation and estimation of functions with structured singularities by deep neural networks

Functions with structured singularities appear in many application domains. For example, in image processing, jumps in intensity value are often associated to the boundaries of physical objects and appear along curves. In classification problems, decision boundaries are often assumed to possess a certain regularity. Finally, in the modelling of physical processes, such as fracture mechanics, singularities naturally appear. In the associated application areas, it is then necessary to finely resolve the singularities. We will analyse the extent to which deep neural networks are affected by discontinuous target functions if the discontinuity admits certain regularities. We will demonstrate that deep neural networks are surprisingly efficient at resolving discontinuities of potentially very high dimensional functions. 

Yan Dolinsky (Hebrew University of Jerusalem)

Tba.

Khoa N Le (TU Berlin)

[The talk takes place on site]

Taming singular SDEs numerically

David Criens (University of Freiburg)

[The talk takes place on site]

Kristin Kirchner (TU Delft)