Brownian motion is an example of a stochastic process. Brownian motion $B_t$ is a stochastic process on $[0,\infty)$ with the following properties:
$B_0=0$ almost surely.
The increments $B_t-B_s$ are independent and normally distributed $N(0,t-s)$ for $t \gt s$.
The function $t\mapsto B_t$ is continuous.
Introduction:
History:
See also:
Wikipedia, Brownian motion
Wikipedia, Wiener process
Last revised on November 30, 2023 at 09:29:38. See the history of this page for a list of all contributions to it.