2 citations · 7 across the 10 of their papers we have counts for
12 papers
Invasion dynamics with vanishing fitness for a quasi-critical birth-death process
Vincent Bansaye, Nadia Belmabrouk, Xavier Erny +1
We study the invasion dynamics of populations exhibiting positive density-dependent effects. We start with a single individual and consider a single-type birth and death process. T…
The first Fundamental Theorem of Calculus for functions defined on Wasserstein space
Xavier Erny
We study two analytical questions concerning functions defined on Wasserstein space. First, we establish an analogue of the first fundamental theorem of calculus in this setting. P…
Generators of measure-valued jump diffusions and convergence rate of diffusive mean-field models
Xavier Erny
The paper has two objectives: proving that the rate of convergence in distribution for mean-field models in CLT regime is , and obtaining explicit expressions for the inf…
Sharp approximation and hitting times for stochastic invasion processes
Vincent Bansaye, Xavier Erny, Sylvie Méléard
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a…
Annealed limit for a diffusive disordered mean-field model with random jumps
Xavier Erny
We study a sequence of particle mean-field systems, each driven by simple point processes in a random environment. Each has the same intensity $(f(X^N_{…
Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling
Xavier Erny, Eva Löcherbach, Dasha Loukianova
We consider the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and Löcherbach (2016) and then further studied in Erny, Löcherbach and…
Mean field system of a two-layers neural model in a diffusive regime
Xavier Erny
We study a model of interacting neurons. The structure of this neural system is composed of two layers of neurons such that the neurons of the first layer send their spikes to the…
White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps
Xavier Erny, Eva Löcherbach, Dasha Loukianova
We study the convergence of particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of t…
Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients
Xavier Erny
We study McKean-Vlasov equations where the coefficients are locally Lipschitz continuous. We prove the strong well-posedness and a propagation of chaos property in this framework.…
A convergence criterion for systems of point processes from the convergence of their stochastic intensities
Xavier Erny
We study systems of simple point processes that admit stochastic intensities. We represent these point processes as thinnings of Poisson measures and are interested in a convergenc…
Conditional propagation of chaos for mean field systems of interacting neurons
Xavier Erny, Eva Löcherbach, Dasha Loukianova
We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and Löcherbach (2016) in a diffusive scaling. The system consists of n…
Mean field limits for interacting Hawkes processes in a diffusive regime
Xavier Erny, Eva Löcherbach, Dasha Loukianova
We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic d…