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math.PR2024
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…
math.PR2024
Microscopic derivation of non-local models with anomalous diffusions from stochastic particle systems
Christian Olivera, Marielle Simon
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local s…
math.PR2024
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…