nLab Brownian motion

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.

Related concepts

• Brownian loop soup

References

For now see

• Wikipedia Brownian motion