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Zbl 0995.60076
Bass, Richard F.; Burdzy, Krzysztof
The supremum of Brownian local times on Hölder curves. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 37, No.6, 627-642 (2001); erratum ibid. 38, No.5, 799-800 (2002). ISSN 0246-0203

One denotes by $S_{\alpha}$ the closed unit ball of the space of $\alpha$-Hölder functions. Moreover we denote by $L_{t}^{f}$ the local time of space-time Brownian motion on the curve $f:[0,1]\rightarrow\Bbb R$. The authors prove that the supremum of $L_{1}^{f}$ over $f\in S_{\alpha}$ is finite if $\alpha>1/2$ and infinite if $\alpha<1/2$.
[Mihai Gradinaru (Nancy)]

MSC 2000:: *60J65 Brownian motion
60J55 Additive functionals

Keywords: local time of space-time Brownian motion; Hölder norms

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