Conference Agenda

Session

Sto2: Stochastic analysis and differential equations

Time:

Tuesday, 08/Sept/2026:

1:30pm - 3:30pm

Session Chair: Alexandra Blessing

Location: L602

Session Topics:

Stochastic analysis and differential equations

Presentations

Optimal Control of Stochastic Schrödinger-Type Equations

Hannelore Lisei

Babes-Bolyai University, Romania

In this presentation, we study stochastic nonlinear Schrödinger-type equations driven by fractional Brownian motion. The main novelty lies in a linearization approach for approximating variational solutions. This framework enables the analysis of the associated stochastic optimal control problems, with particular emphasis on the existence and approximation of optimal controls.

Overcoming the spatial order barrier for SPDEs with additive space-time white noise

Helena Katharina Kremp¹, Mate Gerencser², Lukas Anzeletti²

1: TU Berlin, WIAS Berlin, Germany; 2: TU Wien, Austria

When approximating solutions of SPDEs, a basic challenge is that the rate of convergence is limited due to the low time and space regularity of the solution. Considering semilinear SPDEs with additive space-time white noise in space dimension d=1, we introduce a novel numerical scheme which improves the spatial convergence rate from the classical rate 1/2 to rate 3/2. The temporal convergence rate is proven to be 1 for our scheme, which enhances the classical rate 1/4 using ideas of previous works (Jentzen, Kloeden ‘08, Jentzen ’11, Djurdjevac, Kremp, Gerencser '24) . The talk is based on a work in progress together with Lukas Anzeletti and Mate Gerencser.

Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise

Eliseo Luongo

University of Bielefeld, Germany

In the 1960s, Robert Kraichnan introduced an idealized model for passive scalar turbulence, in which the scalar field is advected by a Gaussian velocity that is delta-correlated in time and Hölder continuous in space. Despite its simplicity, the corresponding linear stochastic PDE captures key features of turbulent flows, including anomalous dissipation. Renewed interest in this model followed the work of Coghi and Maurelli (2026), where it was proved that the same transport-type noise restores well-posedness in regimes where the deterministic 2D Euler equations admit non-unique weak solutions.
In this talk, we further develop this line of research by investigating additional properties of the solutions constructed by Coghi and Maurelli. In particular, we present new results on anomalous fractional Sobolev regularity and dissipation of the mean enstrophy for solutions to the 2D Euler equations with rough Kraichnan noise. Time permitting, we will also discuss implications for the well-posedness theory of more singular nonlinear advection models, such as the Surface Quasi-Geostrophic and Incompressible Porous Media equations.
This talk is based on ongoing joint work with L. Galeati and U. Pappalettera.