On low frequency inference for diffusions without the hot spots conjecture

Giovanni S. Alberti; Douglas Barnes; Aditya Jambhale; Richard Nickl

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arXiv · 2410.19393

On low frequency inference for diffusions without the hot spots conjecture

Giovanni S. Alberti·Douglas Barnes·Aditya Jambhale·Richard Nickl

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Abstract

We remove the dependence on the `hot-spots' conjecture in two of the main theorems of the recent paper of Nickl (2024, Annals of Statistics). Specifically, we characterise the minimax convergence rates for estimation of the transition operator $P_{f}$ 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 $P_f\mapsto f$ from $H^2\to H^2$ to $L^1$.

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Giovanni S. Alberti, Douglas Barnes, Aditya Jambhale, Richard Nickl. 2024-10-25. On low frequency inference for diffusions without the hot spots conjecture. https://arxiv.org/abs/2410.19393

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