Related papers: Homogenization for Generalized Langevin Equations …
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…
Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…
By exact projection in phase space we derive the generalized Langevin equation (GLE) for time-filtered observables. We employ a general convolution filter that directly acts on arbitrary phase-space observables and can involve low-pass,…
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of…
In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the…
The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an…
We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known homogenization or Wong--Zakai diffusion approximation…
We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of…
We perform the periodic homogenization (i.e. $\eps\to 0$) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where $\eps$ is a suitable scale parameter. The objective is to investigate the influence of…
We derive a $c-$number Generalised Langevin Equation (GLE) describing the evolution of the expectation values $\left\langle x_{i}\right\rangle_{t}$ of the atomic position operators $x_{i}$ of an open system. The latter is coupled linearly…
We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of…
The Generalized Langevin Equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general non-equilibrium processes. In this approach, a part of the whole system (an…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…
Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic…
This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path $\varepsilon$ and the heterogeneity length scale $\eta$ vanish. No periodicity assumption is made…
Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed…
Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…