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arXiv · 2307.13001

The supremum of Brownian local times on H\"older curves, II

Richard F. Bass·Krzysztof Burdzy
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Abstract

For $f: [0,1]\to \mathbb R$, we consider $L^f_t$, the local time of space-time Brownian motion on the curve $f$. Let ${\cal S}_\alpha$ be the class of all functions whose H\"older norm of order $\alpha$ is less than or equal to 1. We show that the supremum of $L^f_1$ over $f$ in ${\cal S}_\alpha$ is finite if $\alpha>\frac12$.

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Richard F. Bass, Krzysztof Burdzy. 2023-07-23. The supremum of Brownian local times on H\"older curves, II. https://arxiv.org/abs/2307.13001

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