Associated SAiS project

Project B01 develops modern methods for stochastic differential and partial differential equations whose nonlinearities, distribution dependence or low regularity place them outside standard well-posedness theories. The research combines probabilistic representations, analytical estimates and transformation methods to identify meaningful solution concepts and the conditions under which uniqueness, stability or control can be recovered.

Scientific programme

1. Path-distribution-dependent SPDEs and probabilistic representations for nonlinear Fokker–Planck–Kolmogorov equations.
2. The boundary between non-uniqueness and restricted or pathwise uniqueness for SPDEs with low-regularity Kolmogorov operators.
3. Singular stochastic partial differential equations.
4. Rescaling transformations and optimal control for SPDEs and stochastic variational inequalities.
5. Supercritical stochastic differential equations.

These topics address a basic problem in stochastic analysis: how to define, characterize and control dynamics when coefficients or solutions are too irregular for classical methods.

Project facts

Programme	DFG Collaborative Research Centres
Parent centre	CRC 1283 Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications
Subproject	B01
Parent DFG project number	317210226
Parent funding period	2017–2026
SAiS relationship	Associated project; GEPRIS lists Benjamin Gess as an ongoing project head

SAiS relationship

Research areas

Official sources

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