We remove the dependence on the ‘hot-spots’ conjecture in two of the main theorems of the recent paper of Nickl (2024). Specifically, we characterise the minimax convergence rates for estimation of the transition operator Pf arising from the Neumann Laplacian with diffusion coefficient f on arbitrary convex domains with smooth boundary, and further show that a general Lipschitz stability estimate holds for the inverse map Pf ↦ f from H2 → H2 to L1.
On low frequency inference for diffusions without the hot spots conjecture
Alberti Giovanni S.;
2025-01-01
Abstract
We remove the dependence on the ‘hot-spots’ conjecture in two of the main theorems of the recent paper of Nickl (2024). Specifically, we characterise the minimax convergence rates for estimation of the transition operator Pf arising from the Neumann Laplacian with diffusion coefficient f on arbitrary convex domains with smooth boundary, and further show that a general Lipschitz stability estimate holds for the inverse map Pf ↦ f from H2 → H2 to L1.
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