Near-Minimax Estimation of McKean–Vlasov Diffusions via Sparse ReQU Networks
lihua_lei_stat · x · 2026-09-05
A new statistical framework studies nonparametric inference for density-dependent McKean–Vlasov diffusions, where the drift depends on the process's own density: dXₜ = −Ξ(pₜ(Xₜ))∇V(Xₜ)dt + √2 dWₜ.
Using independent observations at a common time, the authors construct a sieve MLE based on sparse ReQU neural networks, achieving near-minimax optimal rates for estimating both the drift coefficient and the stationary density. The work bridges statistics (nonparametric estimation, likelihood inference, invariant-density estimation), probability (interacting stochastic systems, nonlinear diffusions), and machine learning (neural network approximation).
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