SFB/Transregio 388 investigates the interplay between rough analysis and stochastic dynamics. Central aspects include rough paths and subsequent developments for nonlinear stochastic partial differential equations. The theory of signatures and rough volatility also provides important connections to algebra, statistics, and financial mathematics.

Website: https://sites.google.com/view/trr388/
The group ‘Numerical analysis of stochastic and deterministic partial differential equations’ at Freie Universität Berlin (https://www.mi.fu-berlin.de/math/groups/naspde ) focuses on applied and computational mathematics, in particular optimization, inverse problems and uncertainty quantification.

Job description:
This project aims to provide a new perspective on the classical theory of Bayesian methods for solving complex problems, such as parameter identification of SDE/PDE, nonlinear regression, and inverse problems. Bayesian methods offer a unified framework for addressing these issues through the posterior distribution and are used in many applications. However, rigorous theoretical justification and validation proofs are limited to special cases. The general goal of this project is to extend the existing theory to a broader class of models, including stochastic and rough path systems. The focus is on discretely observed multidimensional SDEs and McKean-Vlasov SDEs. The third-party funded research project provides an opportunity to do a doctorate.

Requirements:
A completed scientific university degree (master’s degree) in mathematics or a closely related field is required.

Desirable:
Solid mathematics education (focus on numerical analysis, functional analysis or stochastic analysis), programming experience.

For further information, please contact Prof. Dr. Claudia Schillings (c.schillings@fu-berlin.de / +4930-83875803).