Published · Journal of Mathematical Fluid Mechanics 25, 28 (2023). A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative transport noise is analysed. This popular intermediate complexity model describes large scale atmosphere and ocean dynamics at the mid-latitudes. The transport…
Published · Stochastic Transport in Upper Ocean Dynamics, Mathematics of Planet Earth 10, pp. 69–85 (2023).
Published · The annals of probability, 52 (2024) 5, pp. 1903-1953. Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the…
Published · Probability theory and related fields, 192 (2025) 3/4, pp. 1447-1515. The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
Published · Stochastics and Partial Differential Equations: Analysis and Computations 12(2), 1046–1099 (2024). We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the…
Published · Information Geometry (2023). The natural gradient field is a vector field that lives on a model equipped with a distinguished Riemannian metric, e.g. the Fisher-Rao metric, and represents the direction of steepest ascent of an…
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and uniqueness of invariant measures, as well…
We consider the nonlinear Kolmogorov equation posed in a Hilbert space $H$, not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework of weak convergence rates of stochastic wave models. Here, we…
Published · Reinforcement Learning and Decision Making (RLDM 2022), extended abstract. Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in the case of partially observable Markov decision…
Published · Annals of Applied Probability 34(2), 2136–2189 (2024). In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to…
We provide nonlinear generalizations of a class of stochastic Gronwall inequalities that have been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a…
Published · Annales de l’Institut Henri Poincaré B 61(3), 1845–1877 (2025). We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned to never being absorbed, the…
