相关论文: Reductions and deviations for stochastic partial d…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative It\^o noise is studied. In particular, we show that there exists a finite range of noise intensities…
In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation.…