Related papers: Stochastic reaction-diffusion equations on network…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
We introduce a stochastic nonlocal reaction--diffusion model arising in tumour dynamics. Spatial dispersal is described by the fractional Laplacian, accounting for anomalous diffusion and long--range relocation events. The system is…
A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network, and can exit the network through the output edges. Each…
In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error…
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases…
The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a…
We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equations driven by nonlinear multiplicative noise, where the…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We study a stochastic linear evolution equation $dX+A(t)Xdt=F(t)dt+ G(t)dw_t$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The…