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.
For now see
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