Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Location indicates the building first and then the room number!

Click on "Floor plan" for orientation in the builings and on the campus.

 
Only Sessions at Location/Venue 
 
 
Session Overview
Session
S 3 (1): Stochastic Analysis and S(P)DEs
Time:
Tuesday, 11/Mar/2025:
4:20 pm - 6:00 pm

Session Chair: Vitalii Konarovskyi
Session Chair: Aleksandra Zimmermann
Location: POT 151
Floor plan

Potthoff Bau
Session Topics:
3. Stochastic Analysis and S(P)DEs

Show help for 'Increase or decrease the abstract text size'
Presentations
4:20 pm - 4:45 pm

Optimal Control of a fractional Noise-Perturbed Nonlinear Schroedinger Equation

Wilfried Grecksch

Martin-Luther-University Halle-Wittenberg

An optimal control problem for a class of stochastic Schroedinger equations with power-type nonlinearity driven by a multiplicative fractional Brownian motion with Hurst index $H \in (0, 1)$ is discussed. The state equation is defined in variational sense. A separation approach is used and the solution is given by the product of the solution of a controlled pathwise problem and the solution of an SDE. A general cost function for the optimal control problem is introduced. Finite dimensional Galerkin approximations and a linearization method are presented and used to derive $\varepsilon$-optimal solutions. \\

This talk is based on joint work with Hannelore Lisei.



4:45 pm - 5:10 pm

Finite Dimensional Projections of HJB Equations in the Wasserstein Space

Andrzej Swiech, Lukas Wessels

Georgia Institute of Technology, United States of America

In this talk, we consider the optimal control of particle systems with mean-field interaction and common noise, and their limit as the number of particles tends to infinity. First, we prove the convergence of the value functions $u_n$ corresponding to control problems of $n$ particles to the value function $V$ corresponding to an appropriately defined infinite dimensional control problem. Then, we prove, under certain additional assumptions, $C^{1,1}$ regularity of $V$ in the spatial variable.

In the second part, we discuss conditions under which the value function $V$ projects precisely onto the value functions $u_n$. Using this projection property, we show that optimal controls of the finite dimensional problem correspond to optimal controls of the infinite dimensional problem and vice versa.

This talk is based on [A. Swiech, L. Wessels: Finite Dimensional Projections of HJB Equations in the Wasserstein Space, https://arxiv.org/abs/2408.07688, 2024].


5:10 pm - 5:35 pm

On the maximal regularity of SPDEs on non-smooth domains

Petru A. Cioica-Licht

Universität Kassel, Germany

Although there exists an almost fully-fledged $L_p$-theory for (semi-)linear second order stochastic partial differential equations (SPDEs, for short) on \textit{smooth} domains, very little is known about the regularity of these equations on \textit{non-smooth} domains. As it is already known from the deterministic theory, boundary singularities like corners, edges, or cusps may have a negative effect on the regularity of the solution. For stochastic equations, this effect comes on top of the already known incompatibility of noise and boundary condition. In this talk I will present some new results towards a better understanding of the impact of these effects on the behaviour of solutions to SPDEs on domains with corners and edges, as they naturally appear in applications.

This is joint work with Emiel Lorist (TU Delft), Mark Veraar (TU Delft), and Tobias Werner (Universität Kassel),



5:35 pm - 6:00 pm

Solution theory for the stochastic thin film equation with spatially colored noise

Antonio Agresti1, Konstantinos Dareiotis2, Benjamin Gess3,4, Manuel Victor Gnann1, Max Sauerbrey4

1TU Delft, Netherlands; 2University of Leeds, United Kingdom; 3Universität Bielefeld, Germany; 4MPI MiS Leipzig, Germany

We present recent results on the existence and uniqueness of solutions to stochastic thin-film equations with spatially colored Gaussian noise. We focus on difficulties related to closing relevant energy and (alpha-) entropy estimates for the equation when subjected to nonlinear gradient noise. Subsequently, we present resulting theorems on the existence of weak solutions and the existence/uniqueness of strong solutions to the equation under various model assumptions.

(This talk summarizes the research works making up the PhD thesis of the 5th author, which is available at the repository of the TU Delft: https://repository.tudelft.nl)


 
Contact and Legal Notice · Contact Address:
Conference: GPSD 2025
Conference Software: ConfTool Pro 2.8.105
© 2001–2025 by Dr. H. Weinreich, Hamburg, Germany