Category:Definitions/Random Walks

This category contains definitions related to Random Walks.
Related results can be found in Category:Random Walks.

One-Dimensional Random Walk

Let $\sequence {X_n}_{n \mathop \ge 0}$ be a Markov chain whose state space is the set of integers $\Z$.

Let $\sequence {X_n}$ be such that $X_{n + 1}$ is an element of the set $\set {X_n + 1, X_n, X_n - 1}$.

Then $\sequence {X_n}$ is a one-dimensional random walk.