Related papers: Large deviations and averaging for systems of slow…

This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical…

We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanisms (Glauber dynamics). Previous results…

We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…

It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is…

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an…

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…

We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…