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Published in:
2014 | OriginalPaper | Chapter
4. The Arcsine Laws for the One-Dimensional Simple Symmetric Random Walk
Author : Ross G. Pinsky
Published in: Problems from the Discrete to the Continuous
Publisher: Springer International Publishing
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Abstract
The simple, symmetric random walk
{S
n
}
n = 0
∞
on \(\mathbb{Z}\) starts at step n = 0 at \(0 \in \mathbb{Z}\) and at each successive step jumps one unit to the right or left, each with probability \(\frac{1} {2}\). The random walk is called “simple” because the sizes of its jumps are restricted to the set {1, −1}. One way to realize this random walk is as follows.