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Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

Statistical Mechanics · Physics 2024-06-24 Jérémie Klinger , Grant M. Rotskoff

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…

Statistical Mechanics · Physics 2007-05-23 M. Annunziato , P. Grigolini , J. Riccardi

We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…

Probability · Mathematics 2024-11-05 Solesne Bourguin , Konstantinos Spiliopoulos

In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…

Probability · Mathematics 2021-10-15 Shivam Dhama , Chetan D. Pahlajani

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…

Numerical Analysis · Mathematics 2018-06-13 Zuzana Majdisova , Vaclav Skala

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a step-like initial density profile. We analytically determine the variance of the current fluctuations for a…

Statistical Mechanics · Physics 2015-06-05 P. L. Krapivsky , Baruch Meerson

We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws…

Methodology · Statistics 2017-01-24 Omiros Papaspiliopoulos , Gareth O. Roberts , Kasia B. Taylor

Considering the natural ventilation, the thermal behavior of buildings can be described by a linear time varying model. In this paper, we describe an implementation of model reduction of linear time varying systems. We show the consequences…

Computational Engineering, Finance, and Science · Computer Science 2012-12-27 Thierry Berthomieu , Harry Boyer

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

Probability · Mathematics 2024-12-31 Saber Jafarizadeh

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

Functional Analysis · Mathematics 2018-03-13 Richard C. Kraaij

In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…

Numerical Analysis · Mathematics 2025-06-18 Timo Sprekeler , Han Wu , Zhiwen Zhang

We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…

Analysis of PDEs · Mathematics 2023-02-22 Emeric Bouin , Clément Mouhot

We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…

Statistical Mechanics · Physics 2020-01-22 Jakub Dolezal , Robert L. Jack

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

Methodology · Statistics 2017-04-03 Nina Munkholt Jakobsen , Michael Sørensen

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps…

Probability · Mathematics 2007-05-23 H. Christian Gromoll

In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…

Probability · Mathematics 2022-06-07 Wei Hong , Shihu Li , Xiaobin Sun

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

Probability · Mathematics 2022-05-24 Shuo Yan

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

Numerical Analysis · Mathematics 2026-04-28 Andrea Bonito , Vivette Girault , Diane Guignard

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Analysis of PDEs · Mathematics 2026-04-01 Hideki Murakawa , Florian Salin