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Topic: Brownian motion sample path: fake or genuine?
Replies: 7   Last Post: Apr 3, 2013 8:12 PM

 Messages: [ Previous | Next ]
 Dan Heyman Posts: 178 Registered: 12/13/04
Re: Brownian motion sample path: fake or genuine?
Posted: Apr 3, 2013 10:25 AM

On Wednesday, April 3, 2013 3:17:45 AM UTC-4, 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
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> random bits.
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>
>
> I had 1.8 gigabytes of digital video, which I
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> whittled down to about 2.5 megabytes of "random bits".
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>
>
> 16384 Bernoulli(1205, 1/2) r.v.s were generated,
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> with k in {0, ... 1205} associated
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> to the #0 s minus #1s : 2k-1205 in
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> the range {-1205, -1203, ... -1, 1, 3, 5, ... 1203, 1205}.
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> This number, 2k-1205, stood in for a Gaussian r.v. of
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> mean zero. The result was a random walk with steps
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> of +1 and -1, sampled every 1205 steps;
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> 16384 samples were taken, without counting
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> x(0) = 0 [starting point].
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>
>
>
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> 16384*1205 = 19,742,720 (bits) or 2,467,840 bytes.
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>
>
> The graphic drawn with MatLab is here:
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>
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>
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> http://img203.imageshack.us/img203/9220/brown1.png
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>
>
>
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> Maybe it's a fake, not random.
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> I don't know ...
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>
>
>
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> David Bernier
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>
>
> --
>
> \$apr1\$LJgyupye\$GZQc9jyvrdP50vW77sYvz1

It looks like BM to me too. Do some tests for independent increments and normality of increments over 50 (say) points.

Date Subject Author
4/3/13 David Bernier
4/3/13 David C. Ullrich
4/3/13 David Bernier
4/3/13 Dan Heyman
4/3/13 David Bernier
4/3/13 David Bernier
4/3/13 David Bernier
4/3/13 David Bernier