Brownian motion

Japanese

ブラウン運動

Also known as

Wiener process

Last reviewed

September 24, 2026

This is a draft, shown for review before publication.

Brownian motion is a stochastic process that moves continuously over time, whose increments over non-overlapping periods are independent and normally distributed with mean 0 and variance equal to the length of the period. It is obtained as the limit of a random walk with ever shorter intervals and smaller steps, and is used to model the movement of prices such as stock prices.