相关论文: Large population limits of Markov processes on ran…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
Density dependent Markov population processes in large populations of size $N$ were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution of the differential equations that describe their average…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with linear observations corrupted with independent measurement…
The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
In communication networks structure and dynamics are tightly coupled. The structure controls the flow of information and is itself shaped by the dynamical process of information exchanged between nodes. In order to reconcile structure and…
We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…
We study the asymptotic behaviour of Markov processes on large weighted Erdos-Renyi graphs where the transition rates of the vertices are only influenced by the state of their neighbours and the corresponding weight on the edges. We find…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…