Related papers: An averaging principle for diffusions in foliated …

Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent H\"older continuous coefficients. Sharp convergence rates with order…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of…

Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…

This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of…

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…

In this paper, we study averaging principle for a class of McKean-Vlasov stochastic differential equations (SDEs) that contain multiplicative fractional noise with Hurst parameter $H > $ 1/2 and highly oscillatory drift coefficient. Here…

The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…

This work focuses on topics related to Hamiltonian stochastic differential equations with L\'{e}vy noise. We first show that the phase flow of the stochastic system preserves symplectic structure, and propose a stochastic version of…

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of…

We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational…

We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the…

Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…

We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex…

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of "almost always", the prevalence, has been developped for vectorial spaces. This…

The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…

In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random…

Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…

We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…

We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector…