Definition:Random Walk/One Dimension
< Definition:Random Walk(Redirected from Definition:One Dimensional Random Walk)
Jump to navigation
Jump to search
Definition
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.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): random walk