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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: 3,877 Registered: 12/13/04
Re: Brownian motion sample path: fake or genuine?
Posted: Apr 3, 2013 8:04 PM

On 04/03/2013 03:35 PM, David Bernier wrote:
> 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:
[...]
>>>> The graphic drawn with MatLab is here:
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> http://img203.imageshack.us/img203/9220/brown1.png

[...]
>
>>> 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].

N.B.: This technique was used for B.M. sample #2,
unfortunately rendered as a JPG graphic file ...

>
> 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.

"Sometimes, PNG is superior..." (xkcd cartoon).

"PNG format is a lossless compression file format, which makes it a
common choice for use on the Web. PNG is a good choice for storing line
drawings, text, and iconic graphics at a small file size."

Quoted from
Ref.:
<
http://www.labnol.org/software/tutorials/jpeg-vs-png-image-quality-or-bandwidth/5385/
> .

>
> Sample path #2:
>
> < http://imageshack.us/a/img12/1371/brown2n.jpg >
>
> At t = 77,150, we're at about -1.8 standard deviations.

David Bernier
--
Jesus is an Anarchist. -- J.R.

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