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

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David Bernier

Posts: 3,276
Registered: 12/13/04
Re: Brownian motion sample path: fake or genuine?
Posted: Apr 3, 2013 10:48 AM
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On 04/03/2013 10:25 AM, danheyman@yahoo.com wrote:
> 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
>>
>> 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 : 2k-1205 in
>>
>> the range {-1205, -1203, ... -1, 1, 3, 5, ... 1203, 1205}.
>>
>> This number, 2k-1205, 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.
>


I guess my aim is perfection here ...
My major (and lasting) concern
is that 1205 random coin tosses, used to generate
a displacement from -1205 to 1205 (odd integer values only),
is not exactly a Gaussian random variable.

The second concern is bugs in the "bit-extractor",
and samples-generating C code,
for the 2,468,800-byte file.

Regards,

David Bernier

----------------------------------------
Memo:
$ md5sum jumbleeaster2013
b07de405f0fd718f044f16d2385b92a8 jumbleeaster2013

$ ls -l jumbleeaster2013
-rw-rw-r--. 1 david david 2468800 Apr 2 21:19 jumbleeaster2013



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