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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: 3,396
Registered: 12/13/04
Re: Brownian motion sample path: fake or genuine?
Posted: Apr 3, 2013 3:35 PM
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On 04/03/2013 10:48 AM, David Bernier wrote:
> 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

[...]

>>> The graphic drawn with MatLab is here:
>>>
>>>
>>>
>>>
>>>
>>> http://img203.imageshack.us/img203/9220/brown1.png
>>>
>>>
>>>
>>>
>>>
>>> Maybe it's a fake, not random.

[...]

>> 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.


I used chunks of 32 bytes to get blocks of 256 random bits,
interpreted as a sample from a uniform distribution on
[0, 1].

I used the Box-Muller method to transform pairs
of uniform variates into pairs of standard normal,
independent, variates:
< http://en.wikipedia.org/wiki/Box_Muller_transform#Basic_form > .

Thus, the result is 77,150 independent standard normal variates.

I'm wondering if *.png graphics files might look better
than *.jpg files ... I made them both, brown1 and brown2,
with MatLab on an off-line computer with Windows 2000.

Sample path #2:

< http://imageshack.us/a/img12/1371/brown2n.jpg >

At t = 77,150, we're at about -1.8 standard deviations.

dave




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