On strong invariance for local time of partial sums |
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| Authors: | M. Csörgő P. Révész |
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| Affiliation: | Department of Mathematics and Statistics, Carleton University, Ottawa K1S 5B6, Canada;Mathematical Institute of the Hungarian Academy of Sciences, 1053 Budapest, Reáltanoda u. 13-15, Hungary |
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| Abstract: | For a suitable definition of the local time of a random walk strong invariance principles are proved, saying that this local time is like that of a Wiener process. Consequences of these results are LIL statements for the local time of a general enough class of random walks. One of the tools for our proofs is a discrete version of the Tanaka formula. |
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| Keywords: | Primary 60J55 Secondary 60J65, 60F17 Wiener process Tanaka formula random walk invariance LIL |
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