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The supremum of Brownian local times on H\"older curves, II
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The supremum of Brownian local times on H\"older curves, II
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math.PR
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alphabrownianlocaloldersupremumclassconsidercurve
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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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