Logarithmic scaling of planar random walk's local times

Péter Nándori; Zeyu Shen

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arXiv · 1603.07587

Logarithmic scaling of planar random walk's local times

Péter Nándori·Zeyu Shen

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Abstract

We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the $M1$ topology and fails to hold in the $J1$ topology.

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Péter Nándori, Zeyu Shen. 2016-03-24. Logarithmic scaling of planar random walk's local times. https://arxiv.org/abs/1603.07587

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