Related papers: Discretized Fast-Slow Systems near Transcritical S…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
The equations for the sliding of a single block driven by an elastic force show numerically a fast and a slow step in their dynamics when a dimensionless parameter is very large, a limit pertinent for many applications. An asymptotic…
In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
We analyze continuous-time models of accelerated gradient methods through deriving conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics of $X(t)$, we analyze the dynamics of $W(t)=t^\alpha(X(t)-X_c)$…
Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization cannot be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for…
We study single-loop gradient-flow dynamics for nested optimization, where the outer variable evolves while auxiliary variables track the inner solution map. While existing analyses typically rely on problem- and condition-specific Lyapunov…
In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their…
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…
Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al.…
We extend the Lyapunov stability criterion to Euler discretizations of differential inclusions. It relies on a pair of Lyapunov functions, one in continuous time and one in discrete time. In the context of optimization, this yields…
We present the first review of methods to overapproximate the set of reachable states of linear time-invariant systems subject to uncertain initial states and input signals for short time horizons. These methods are fundamental to…
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may…
We investigate the spreading of passive tracers in closed basins. If the characteristic length scale of the Eulerian velocities is not very small compared with the size of the basin the usual diffusion coefficient does not give any relevant…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…