Minimum curvature flow and martingale exit times

Larsson, Martin and Ruf, Johannes ORCID: 0000-0003-3616-2194 (2024) Minimum curvature flow and martingale exit times. Electronic Journal of Probability, 29. ISSN 1083-6489

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Abstract

We study the following question: What is the largest deterministic amount of time T∗ that a suitably normalized martingale X can be kept inside a convex body K in R d ? We show, in a viscosity framework, that T∗ equals the time it takes for the relative boundary of K to reach X(0) as it undergoes a geometric flow that we call (positive) minimum curvature flow. This result has close links to the literature on stochastic and game representations of geometric flows. Moreover, the minimum curvature flow can be viewed as an arrival time version of the Ambrosio–Soner codimension-(d − 1) mean curvature flow of the 1-skeleton of K. Our results are obtained by a mix of probabilistic and analytic methods.

Item Type:	Article
Additional Information:	© 2024 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	27 Jun 2024 08:51
Last Modified:	12 Dec 2024 04:21
URI:	http://eprints.lse.ac.uk/id/eprint/123987

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