Markovian dynamics under model uncertainty
A talk in the CRC Seminar series by
Max Nendel
| Abstract: | When considering stochastic processes for the modeling of real world phenomena, a major issue is so-called model uncertainty or epistemic uncertainty. The latter refer to the impossibility of perfectly capturing information about the future in a single stochastic framework. In a dynamic setting, this leads to the task of constructing consistent families of nonlinear transition semigroups. In this talk, we present two ways to incorporate model uncertainty into a Markovian dynamics. One approach considers parameter uncertainty in the generator of a Markov process while the other considers perturbations of a reference model within a Wasserstein proximity. We show that, in typical situations, these two a priori different approaches de facto lead to the same nonlinear transition semigroup. In a last step, we discuss implications, possible extensions, and research questions that we aim to investigate in the CRC’s project C7. The talk is based on joint works with Robert Denk, Sven Fuhrmann, Ben Goldys, Michael Kupper, and Michael Röckner.
Zoom Meeting ID: 951 0299 5070 Passcode: 892089 $\href{ https://uni-bielefeld.zoom.us/j/95102995070?pwd=NFZHb1BMZTZyTVRkREdrNFZjWkx4dz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): C7 |