Published · Nonlinear differential equations and applications, 33 (2026) 2, p. 52. We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions on the turning kernel and…
We consider the focusing power nonlinearity heat equation in dimensions $d \geq 3$. It is well-known that if $p$ is large enough then \eqref{Eq:Heat_abstract} is unconditionally locally well-posed in $L^q(\mathbb{R}^d)$ for $q \geq d(p-1)/2$. We prove that this result is…
Published · Stochastics and Partial Differential Equations: Analysis and Computations 13(2) (2025), 956–1033. Using the method of paracontrolled distributions, we show the local well-posedness of an additive noise approximation to the fluctuating hydrodynamics of the Keller-Segel model on the two-dimensional torus. Our approximation is a…
Published · Proceedings of the 42nd International Conference on Machine Learning, PMLR 267 (2025). Reinforcement Learning (RL) agents can solve diverse tasks but often exhibit unsafe behavior. Constrained Markov Decision Processes (CMDPs) address this by enforcing safety constraints, yet existing methods either sacrifice reward maximization or…
Published · Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388. The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes…
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a $d$-dimensional discrete torus is proven. The argument is based on a comparison of the generators of the density fluctuation field of the SSEP and the generalized Ornstein-Uhlenbeck process,…
For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these settings, it is vital to study to which minimum an optimization algorithm converges. The possibility of having…
Published · Probability Theory and Related Fields (2026). In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic…
Published · Nonlinearity 38, 075023 (2025). In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a…
Published · SIAM Journal on Mathematical Analysis 57(3), 3071–3109 (2025). We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy…
Published · Stochastic processes and their applications, 193 (2026), p. 104847. Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of…
