Brownian motion can feel the shape of a drum

Renan Gross

Stochastic Processes and their Applications, 2024, vol. 167, issue C

Abstract: We study the scenery reconstruction problem on the d-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.

Keywords: Scenery reconstruction problem; Infinite Vandermonde matrix; Brownian motion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104233

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