Proceedings of the American Mathematical Society· 2026Q1
On the slow points of fractional Brownian motion
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- 2026year
Short summary
A new method, inspired by SPDE theory, computes the Hausdorff dimension of slow points in fractional Brownian motion (fBm).
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Key points
- Introduces a new method for studying slow points in fractional Brownian motion (fBm).
- The method is inspired by recent ideas on points of slow growth for SPDEs.
- Enables the computation of the Hausdorff dimension of fBm slow points.
- Requires new localization ideas with potential for broader applications.
AI-generated from the title and abstract; the full text is not read.
Abstract
Esser and Loosveldt have recently resolved a long-standing open problem in the folklore by proving that fractional Brownian motion (fBm) has slow points in the sense of Kahane, following a rich theory of slow points developed for Brownian motion and other, related, self-similar Markov processes. We presently introduce another method for the study of slow points in order to compute the Hausdorff dimension of fBm slow points. Our method follows recent ideas on the points of slow growth for SPDEs but also requires a number of new localization ideas that are likely to have other applications.
The authors' abstract, as published at the source. Proceedings of the American Mathematical Society, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance