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Nonparametric inference for density-dependent McKean--Vlasov diffusions

arXiv · AI, language, vision and robotics · article · Sep 1, 2026 · UTC

The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density. Under certain assumptions on the (known) potential, we reduce the problem to the one-dimensional one and construct a sieve maximum-likelihood estimator based on sparse ReQU neural networks subject to structural and Hölder constraints. Using the endpoint-adapted graded approximation, we achieve the rate of $\left(b_n\log n/n\right)^{2(β+1)/(2β+3)}$ for the Kullback-Le

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