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…
Published · Real Analysis Exchange 48(1), 101–106 (2023). In this paper we answer a question raised by David H. Fremlin about the Hausdorff measure of $\mathbb{R}^2$ with respect to a distance inducing the Euclidean topology. In particular we prove that the Hausdorff $n$-dimensional measure of $\mathbb{R}^n$ is never…
Published · Journal of Differential Equations 392, 74–127 (2024). We provide generalizations of a class of stochastic Gronwall inequalities that has been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This…
Published · Journal of Differential Equations 389, 114–149 (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 Navier-Stokes equations with additive noise and no-slip boundary conditions to the solution of the corresponding…
Published · Advances in Continuous and Discrete Models (2022). We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-Laplace equation or the Modica-Mortola energy with essential or natural…
Published · Stochastic Processes and their Applications 157, 376–412 (2023). We construct and analyze the Jacobi process – in mathematical biology referred to as Wright-Fisher diffusion – using a Dirichlet form. The corresponding Dirichlet space takes the form of a Sobolev space…
Published · International Conference on Learning Representations (ICLR 2022). We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted…
Published · The annals of probability, 50 (2022) 6, pp. 2288-2343. We prove optimal regularity estimates in Sobolev spaces in time and space for solutions to stochastic porous medium equations. The noise term considered here is multiplicative, white in time and coloured in…
