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 Electronic Journal of Probability > Vol. 3 (1998) > Paper 14 open journal systems 


Large Favourite Sites of Simple Random Walk and the Wiener Process

Endre Csáki, Hungarian Academy of Sciences
Zhan Shi, Université de Paris VI


Abstract
Let $U(n)$ denote the most visited point by a simple symmetric random walk ${ S_k}_{kge 0}$ in the first $n$ steps. It is known that $U(n)$ and $max_{0le kle n} S_k$ 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.


Full text: PDF

Pages: 1-31

Published on: September 30, 1998
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Electronic Journal of Probability. ISSN: 1083-6489