An elementary approach to Brownian local time based on simple,symmetric random walks |
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| Authors: | Tamás Szabados Balázs Székely |
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| Affiliation: | (1) Department of Mathematics Budapest University of Technology and Economics, Műegyetem rkp. 3, H ép. V em. H-1521 Budapest Hungary;(2) Budapest University of Technology and Economics, Műegyetem rkp. 3. H-1521 Budapest Hungary |
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| Abstract: | Summary 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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| Keywords: | random walk local time Brownian motion strong approximation |
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