arXiv subjects

Alexandre B. de Souza

Publications and source records attributed to Alexandre B. de Souza.

4 recordsLinked to original sources

arXiv2026

Pathwise quantitative particle approximation of nonlinear stochastic Fokker-Planck equations via relative entropy

We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique strong solution to the associated Fokker-Planck equation. Our proof is based on tools from PDE analysis, stochastic analysis, functional inequalities, and also we use the dissipation of entropy which provides some bound on the Fisher information of the particle system. The approach applies to repulsive and attractive kernels.

math.PR↗

arXiv2026

Quantitative propagation of chaos for 2D stochastic vortex model on the whole space under moderate interactions

We derive the stochastic 2D vortex model on the whole Euclidean space from moderately interacting particle systems driven by individual and environmental noises, obtaining quantitative estimates in the sense of the entropy and energy functionals. The main novelties lie in combining the control of the Fisher information of the particle system with the Ladyzhenskaya and Donsker-Varadhan inequalities, as well as localization techniques within the probabilistic data setting, to address the nonlinearity and quadratic variation arising from Ito's formula. Moreover, we construct a suitable solution for the limiting process.

math.AP↗

arXiv2025

Convergence Rate for Moderate Interaction particles and Application to Mean Field Games

We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate depends on the moderate scaling parameter, the regularity of the solution of the limit equation and the dimension. Our approach is based on the techniques of stochastic calculus, some properties of Besov and Triebel-Lizorkin space, and the semigroup approach introduced in [9].

math.PR↗

arXiv2024

Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel

We derive quantitative estimates for large stochastic systems of interacting particles perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We prove that the (mollified) empirical process converges to the solution of the nonlinear stochastic Fokker-Planck equation. The proof is based on Itô's formula for $H_{q}^{1}$-valued process, commutator estimates, and some estimations for the regularization of the empirical measure. Moreover, we show that the aforementioned equation admits a unique strong solution in the probabilistic sense. The approach applies to repulsive and attractive kernels.

math.PR↗