相关论文: On the Hill relation and the mean reaction time fo…

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…

Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and…

Various processes can be modelled as quasi-reaction systems of stochastic differential equations, such as cell differentiation and disease spreading. Since the underlying data of particle interactions, such as reactions between proteins or…

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…

A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…

We consider in this paper a stochastic process that mixes in time, according to a nonobserved stationary Markov selection process, two separate sources of randomness: i) a stationary process which distribution is accessible (gold standard);…

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…

A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…

We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a…

We use a Hamiltonian interacting particle system to derive a stochastic mean field system whose McKean-Vlasov equation yields the incompressible Navier Stokes equation. Since the system is Hamiltonian, the particle relabeling symmetry…

We study metastable behaviour in systems of weakly interacting Brownian particles with localised, attractive potentials which are smooth and globally bounded. In this particular setting, numerical evidence suggests that the particles…

This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approximate specific queues on R with one-sided L\'evy input, such as…

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such…

This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process algebra models. In particular, we have proved the uniform…

Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…

We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…

We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms,…

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based…

The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the…