相关论文: Limit theorems for sticky SDEs with local times an…

We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precise characterization of the limiting joint distribution as a…

We establish the consistency of a local time approximation of a diffusion at a sticky threshold based on high-frequency observations. First, we prove the result for sticky Brownian motion, and then extend it to It\^o diffusions with a…

We study a class of high-frequency path functionals for diffusions with singular thresholds or boundaries, where the process exhibits either (i) skweness, oscillating coefficients, and stickiness, or (ii) sticky reflection. The functionals…

The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…

We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…

We present a first-principles formalism for studying dynamical heterogeneities in glass forming liquids. Based on the Non-Equilibrium Self-Consistent Generalized Langevin Equation theory, we were able to describe the time-dependent local…

The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…

We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…

Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…

We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…

In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…

The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…

The existence of a generalized fluctuation-dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the…

We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations.…

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…