相关论文: A global method for deterministic and stochastic h…
In this note, we study an infinite reaction network called the stochastic Becker-D\"oring process, a sub-class of the general coagulation-fragmentation models. We prove pathwise convergence of the process towards the deterministic…
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 consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, C. R. Acad. Sci. Serie I 2006 and Journal de Mathematiques Pures et Appliquees 2007]. The equation under consideration is a…
In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences…
In recent years, many difficulties appeared when taking into account the inherent stochastic behavior of neurons and voltage-dependent ion channels in Hodgking-Huxley type models. In particular, an open problem for a stochastic model of…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic…
We study the homogenization of an obstacle problem in a perforated domain. The holes are periodically distributed but have random size and shape. The capacity of the holes is assumed to be stationary ergodic. As in the periodic case, we…
We introduce a new method for obtaining quantitative results in stochastic homogenization for linear elliptic equations in divergence form. Unlike previous works on the topic, our method does not use concentration inequalities (such as…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with…
We consider the homogenization of monotone systems of viscous Hamilton-Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic…
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates…
The superiority of stochastic symplectic methods over non-symplectic counterparts has been verified by plenty of numerical experiments, especially in capturing the asymptotic behaviour of the underlying solution process. How can one…
We show existence and uniqueness of invariant measures for SDE of the form \[ dX_t = g(X_t)dt + u(X_t)dt + dW^H_t \] where $W^H$ is a fractional Brownian motion (fBm) with Hurst parameter $H\in (0,\frac{1}{2})$, $u$ is a linearly dispersive…
We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…
We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set. Our contributions are twofold. First, we establish…