Work

On low frequency inference for diffusions without the hot spots conjecture

Year: 2025

Type: article

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 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} .

Source: Mathematical Statistics and Learning

DOI: 10.4171/msl/53

Authors: Giovanni S. Alberti, Douglas Barnes, Aditya Jambhale, Richard Nickl

Institutions: University of Genoa, University of Cambridge

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

Award: G1043805054