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1998 Large Favourite Sites of Simple Random Walk and theWiener Process
Endre Csaki, Zhan Shi
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Electron. J. Probab. 3: 1-31 (1998). DOI: 10.1214/EJP.v3-36


Let $U(n)$ denote the most visited point by a simple symmetric random walk $\{ S_k\}_{k\ge 0}$ in the first $n$ steps. It is known that $U(n)$ and $max_{0\le k\le n} S_k$ satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. Lévy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The corresponding problem for the Wiener process is also studied.


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Endre Csaki. Zhan Shi. "Large Favourite Sites of Simple Random Walk and theWiener Process." Electron. J. Probab. 3 1 - 31, 1998.


Accepted: 30 September 1998; Published: 1998
First available in Project Euclid: 29 January 2016

zbMATH: 0908.60070
MathSciNet: MR1646468
Digital Object Identifier: 10.1214/EJP.v3-36

Primary: 60J55
Secondary: 60J15 , 60J65

Keywords: favourite site , Local time , Random walk , Wiener process

Vol.3 • 1998
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