An elementary approach to Brownian local time based on simple, symmetric random walks

Tamas Szabados; Balazs Szekely

doi:10.1007/s10998-005-0022-8

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arXiv · 1008.1701

An elementary approach to Brownian local time based on simple, symmetric random walks

Tamas Szabados·Balazs Szekely

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Abstract

In this paper we define Brownian local time as the almost sure limit of the local times of a nested sequence of simple, symmetric random walks. The limit is jointly continuous in $(t,x)$. The rate of convergence is $n^{\frac14} (\log n)^{\frac34}$ that is close to the best possible. The tools we apply are almost exclusively from elementary probability theory.

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BibTeX RIS

Tamas Szabados, Balazs Szekely. 2010-08-10. An elementary approach to Brownian local time based on simple, symmetric random walks. https://doi.org/10.1007/s10998-005-0022-8

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