The supremum of Brownian local times on Holder curves

Richard Bass; Krzysztof Burdzy

doi:10.1016/S0246-0203(00)01072-4

The supremum of Brownian local times on Holder curves

Probability 2015-06-26 v1

Authors: Richard Bass , Krzysztof Burdzy

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

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

Keywords

Brownian local time space-time Brownian motion Hölder curves Hölder norm supremum

Cite

@article{arxiv.math/0002012,
  title  = {The supremum of Brownian local times on Holder curves},
  author = {Richard Bass and Krzysztof Burdzy},
  journal= {arXiv preprint arXiv:math/0002012},
  year   = {2015}
}

Related papers

View all related →