Scaling limit of the local time of the $(1,L)-$random walk

Wenming Hong; Hui Yang

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arXiv · 1402.3949

Scaling limit of the local time of the $(1,L)-$random walk

Wenming Hong·Hui Yang

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Abstract

It is well known (Donsker's Invariance Principle) that the random walk converges to Brownian motion by scaling. In this paper, we will prove that the scaled local time of the $(1,L)-$random walk converges to that of the Brownian motion. The results was proved by Rogers (1984) in the case $L=1$. Our proof is based on the intrinsic multiple branching structure within the $(1,L)-$random walk revealed by Hong and Wang (2013).

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Wenming Hong, Hui Yang. 2014-02-17. Scaling limit of the local time of the $(1,L)-$random walk. https://arxiv.org/abs/1402.3949

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