4 papers
Pathwise quantitative particle approximation of nonlinear stochastic Fokker-Planck equations via relative entropy
Christian Olivera, Alexandre B. de Souza
We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantita…
Quantitative propagation of chaos for 2D stochastic vortex model on the whole space under moderate interactions
Alexandre B. de Souza
We derive the stochastic 2D vortex model on the whole Euclidean space from moderately interacting particle systems driven by individual and environmental noises, obtaining quantita…
Convergence Rate for Moderate Interaction particles and Application to Mean Field Games
Josué Knorst, Christian Olivera, Alexandre B. de Souza
We study two interacting particle systems, both modeled as a system of stochastic differential equations driven by Brownian motions with singular kernels and moderate interacti…
Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel
Josué Knorst, Christian Olivera, Alexandre B. de Souza
We derive quantitative estimates for large stochastic systems of interacting particles perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We pro…