Regularization by noise in discrete and continuous systems

01.10.2021–30.09.2025
FWF Principal Investigator projects
Principal investigator: Mate GERENCSER (E101-01)

When a system is stuck in an unfavourable state, an external force can push it out of it and the system goes on to behave in a much more favourable way. One may think of the classical example of an old TV screen seemingly stuck on a grainy picture, which is suddenly fixed if one "perturbs" the TV device with an appropriately placed hit. In the mathematical context of the project, the role of these perturbations is played by random processes. A wide variety of real-world phenomena is described by random processes. These dynamics are characterised by being driven by a very large number of very small random influences. For example, in financial markets the cumulative effects high-frequency micro-transactions influence the evolution of the prices of financial instruments. Leveraging how these small random oscillations force stochastic processes into favourable behaviour is called regularisation by noise. Our project studies the theory, analysis, and computational treatment of stochastic differential equations with such effects.

The project has recently entered in its last year. With the involvement of 2 full-time postdocs, 1 part-time postdoc, and 1 student assistant, we have so far finished 11 articles, many of them already published in leading journals like Annals of Probability, Forum of Mathematics Sigma, or SIAM Journal of Numerical Analysis. To conclude a successful 4 years, make our contributions visible, and initiate new directions in the field, we are organizing a workshop next April, where over 20 invited speakers have already confirmed their participation, featuring prominent figures of the field such as Nicolai KRYLOV, Michael RÖCKNER oder Alexander VERETENNIKOV.

Project members: Helena KREMP, Chengcheng LING, Lukas ANZELETTI, Gerald LAMPL