Nonparametric inference on Fokker-Plank and McKean-Vlasov models

Adriana Laurindo Monteiro; Roberto Imbuzeiro Oliveira

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arXiv · 2606.14514

Nonparametric inference on Fokker-Plank and McKean-Vlasov models

Adriana Laurindo Monteiro·Roberto Imbuzeiro Oliveira

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Abstract

We propose a kernel-based estimator of the velocity field governing the transport and diffusion of $d$-dimensional interacting particles. Assuming the initial positions are i.i.d. with law $\mu_0$, we establish consistency of the estimator with an explicit mean-squared error rate of order $h^2 + N^(-2/(d+2))$, where $h$ denotes the time-discretization step and N the number of particles. The analysis covers two distinct settings: the Fokker-Planck equation, where we recover the underlying potential function, and the McKean-Vlasov equation, where we deconvolve the interaction kernel driving the mean-field dynamics.

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Adriana Laurindo Monteiro, Roberto Imbuzeiro Oliveira. 2026-06-12. Nonparametric inference on Fokker-Plank and McKean-Vlasov models. https://arxiv.org/abs/2606.14514

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