The Institute for Statistics and Mathematics is pleased to invite you to this semester’s first research seminar, taking place on campus with the following two talks:

• Paul Eisenberg(Institute for Statistics and Mathematics, WU Vienna)
  Bounds for Expected Occupation Density and Applications
  
  Wednesday, January 14, 2026, 17:15, Building D4, Room D4.0.127
  
  Abstract: Occupation densities (local times) play a central role in the fine analysis of stochastic processes, providing a detailed description of how trajectories distribute mass in space and time. In this presentation, we discuss general bounds for expected occupation densities under minimal regularity and non-degeneracy assumptions. These results yield explicit estimates and clarify how probabilistic features of the underlying dynamics influence concentration behaviour.

  We focus on applications to stochastic control problems and robust finance. In particular, we show how bounds on expected occupation densities provide a priori estimates for controlled dynamics, yielding effective control of state space exploration under admissible strategies and model uncertainty. These pre-estimates can be used to bound cost functionals, control constraint violations, and sensitivities with respect to changes in control policies or probability measures. Such results are especially useful in the analysis of existence, stability, and approximation of optimal controls, as well as in the design of numerical and learning-based methods in stochastic control and robust financial modelling.
  Overall, the talk highlights expected occupation density estimates as a foundational probabilistic tool for deriving robust pre-estimates in stochastic control and related areas.

Please note that currently there are no Zoom streams planned for the talks in this semester.
For further information (such as related papers, linked software etc.) and the seminar schedule, please see:
www.wu.ac.at/en/statmath/research/resseminar