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Aug 6, 2013 at 20:17 comment added john mangual @BS With independent increments, you could pick new Gaussian variables at t=1 and keep going.
Aug 6, 2013 at 14:14 history edited Michael Hardy CC BY-SA 3.0
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Aug 6, 2013 at 13:55 comment added BS. @john : according to the notes (which have some confusing typos), brownian motion (starting at $0$) is given by $a_0t+B(t)-B(0)$ but only for $0\leq t\leq 1$. Here $a_0$ is another standard gaussian.
Aug 6, 2013 at 10:27 comment added john mangual @MichaelHardy The notes say $B(t) - b_0(t)$ is the Brownian motion. The variance of Brownian motion is linear in the time $t$. Then $B(0) = 0$, $B(t)$ is a.s. continuous, independent increments, and $B(t_2) - B(t_1)$ is normal.
Aug 6, 2013 at 4:01 comment added Michael Hardy The series you wrote after "$B(t)=$" is a periodic function, and it is for such functions that Fourier series are defined. But the usual Brownian motion (or Wiener process) is not periodic.
Aug 6, 2013 at 3:58 history edited Michael Hardy CC BY-SA 3.0
It's not actually named after a person named "White", although Brownian motion is named after a person named "Brown".
Aug 5, 2013 at 20:01 history asked john mangual CC BY-SA 3.0