Related papers: A note on scaling limits for truncated birth-and-d…
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
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…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
We consider birth and death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density dependent decreasing death rate. The corresponding statistical…
We study the approximation of a Markov chain on a reduced state space, for both discrete- and continuous-time Markov chains. In this context, we extend the existing theory of formal error bounds for the approximated transient distributions.…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Motivated by various applications, we describe the scaling limits of bivariate Markov chains $(X,J)$ on $\mathbb Z_+ \times \{1,\ldots,\kappa\}$ where $X$ can be viewed as a position marginal and $\{1,\ldots,\kappa\}$ is a set of $\kappa$…
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…