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The supremum of Brownian local times on Hölder curves, II
Richard F. Bass, Krzysztof Burdzy · 2023-07-24 · via math.PR updates on arXiv.org

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 ${\cal S}_α$ be the class of all functions whose Hölder norm of order $α$ is less than or equal to 1. We show that the supremum of $L^f_1$ over $f$ in ${\cal S}_α$ is finite if $α>\frac12$.

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