Related papers: Weak universality for stochastic reaction-diffusio…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
We study the evolution of conditional mutual information in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where conditional mutual information spreads…
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or…
Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…
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…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
In this paper, we investigate the nonlocal reaction-diffusion equation driven by stationary noise, which is a regular approximation to white noise and satisfies certain properties. We show the existence of random attractor for the equation.…
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…
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…
In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction-diffusion equation with a nonlinear multiplicative noise. Also, we establish the existence and uniqueness of solutions and…
A common model of stochastic auto-regulatory gene expression describes promoter switching via cooperative protein binding, effective protein production in the active state and dilution of proteins. Here we consider an extension of this…
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for…
We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…
Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology. When chemical species and reaction rates in a reaction system have different orders of magnitude, the associated…
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…
In this paper, we investigate the uniform large deviation principle of the fractional stochastic reaction-diffusion equation on the entire space R^n as the noise intensity approaches zero. The nonlinear drift term is dissipative and has a…
Doubly nonlinear stochastic evolution equations are considered. Upon assuming the additive noise to be rough enough, we prove the existence of probabilistically weak solutions of Friedrichs type and study their uniqueness in law. This…
In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…
We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…