Random walk
Statement
A random walk is a stochastic process where each step is independent and identically distributed. In one dimension, the position after n steps has mean 0 and variance n. The discrete analogue of Brownian motion; the limit of scaled random walks converges to Wiener process.
Formula
X_n = X_{n-1} + ε_n, ε_n i.i.d.
Equation
X_n = ∑_{i=1}^n ε_i (mean 0, variance n)
Source
K. Pearson, The problem of the random walk, Nature 72, 1905
Domains
mathematics, physics