
Re: Brownian motion sample path: fake or genuine?
Posted:
Apr 3, 2013 10:25 AM


On Wednesday, April 3, 2013 3:17:45 AM UTC4, David Bernier wrote: > I used snow (white noise) from an analog cathode ray tube TV, > > recorded with a webcam, as the source of entropy for supposedly > > random bits. > > > > I had 1.8 gigabytes of digital video, which I > > whittled down to about 2.5 megabytes of "random bits". > > > > 16384 Bernoulli(1205, 1/2) r.v.s were generated, > > with k in {0, ... 1205} associated > > to the #0 s minus #1s : 2k1205 in > > the range {1205, 1203, ... 1, 1, 3, 5, ... 1203, 1205}. > > This number, 2k1205, stood in for a Gaussian r.v. of > > mean zero. The result was a random walk with steps > > of +1 and 1, sampled every 1205 steps; > > 16384 samples were taken, without counting > > x(0) = 0 [starting point]. > > > > > > 16384*1205 = 19,742,720 (bits) or 2,467,840 bytes. > > > > The graphic drawn with MatLab is here: > > > > > > http://img203.imageshack.us/img203/9220/brown1.png > > > > > > Maybe it's a fake, not random. > > I don't know ... > > > > > > David Bernier > > > >  > > $apr1$LJgyupye$GZQc9jyvrdP50vW77sYvz1
It looks like BM to me too. Do some tests for independent increments and normality of increments over 50 (say) points.

