3 papers
math.PR2021
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…
math.PR2019
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…
math.PR2019
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…