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On the Simple Symmetric Random Walk and Its Maximal Function

José Luis Palacios
The American Statistician
Vol. 62, No. 2 (May, 2008), pp. 138-140
Stable URL: http://www.jstor.org/stable/27643992
Page Count: 3
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On the Simple Symmetric Random Walk and Its Maximal Function
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Abstract

For the simple symmetric one-dimensional random walk Sn we derive closed form and asymptotic formulas for E max (Sn, 0), E|Sn|, EMn, $\mathit{EM}_{n}^{2}$, cov(Sn, Mn) and the correlation coefficient of Sn and Mn, where Mn = max {0, S1,...,Sn}, using elementary material in Feller's classic textbook.

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