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Result R5431 on D3360: Standard integer random walk
Subresult of R5430: Growth rate for the expectation of the absolute value of the standard integer random walk

Growth class for the expectation of the absolute value of the standard integer random walk

Formulation 0

Let

$S : \mathbb{N} \to \text{Random} (\mathbb{Z})$ be the D3360: Standard integer random walk.

Then

$\begin{equation} \mathbb{E} |S_N| = O(\sqrt{N}) \end{equation}$

Also known as

Growth class for the expected distance of the standard integer random walk from the origin

Proofs

Proof 0

Let

$S : \mathbb{N} \to \text{Random} (\mathbb{Z})$ be the D3360: Standard integer random walk.

This result is a particular case of R5430: Growth rate for the expectation of the absolute value of the standard integer random walk.

$\square$