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Random Walks In Force Fields


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#1 bizquant

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Posted 16 May 2017 - 05:29 PM

Please see the technical details in there: 

 

<<link removed>>

 

I am pretty sure it would work for stock market, and I think the Wave-Particle PDE is better thank Klein-Gordon PDE. 

 

 

If I am right, Newton & Eisenstein finally meet together at Wall Street in a timeless fashion.. literally time-less.. =)

 

Please do feel free to ask or point out my errors...

 

Thank y'all.. bizquant



#2 Buffy

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Posted 16 May 2017 - 11:56 PM

Hi bizquant, welcome to Hypography.

 

The link to your site was removed, because quite frankly no one is going to click on it without a good reason to 1) be interested in it and 2) until you build some trust the assumption is that it's got a virus behind it.

 

So what you need to do is present your idea here, so we all can read it here rather than clicking all over the internet to make sense of it.

 

Call us lazy, but that's kind of how a discussion forum works.

 

 

 

I am not what you see, I am what time and effort and interaction slowly unveil, :phones:
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#3 bizquant

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Posted 17 May 2017 - 04:24 AM

Dear Buffy,

 

Thanks for your reply. I completely understand. Below is an introduction of the contents extracted from the link, and attach the draft paper in PDF here to assure everyone that this is a legitimate proposal. It'd be great if you can re-instate the link. I wrote 6 chapters of guidelines to introduce this  paper. It is my intent to change people's perception systematically.. below is a starting point:

 

Extract from the link ----------------------------------------------------------------

Brownian Motion is often viewed as the description of observed particles randomly colliding with surrounding particles. And Stochastic process is typically defined as follows: dx=μdt+σdW

 

It is suggesting that Brownian particles randomly collide around a deterministic mean that can change over time. It is however, in violation of Newtonian rules, as particles would not spontaneously know where the mean is, unless some form of force field/velocity gradient are present in the system. 

This article proceeds to model random walks with the potential energy adjustments that can be used to describe a finite entropy system. The diffusion version (1st order) governing PDE is in a form of Reaction-Diffusion process. In the paper, we will lay out the foundation by modeling Brownian particles randomly colliding (diffusion) but pulled to each other by force to deterministic mean in a vacuum, simulated as graph below:
 

2D-Ball_zpsb67a4365.gif

The Stochastic process describing such system should be a Jump-to-mean process where jump arrival rate is determined by spatial velocity gradient, and 

term is Laplace distribution with variance one: dx=(μ-X)dJ+σdξ

 

End of the extract ----------------------------------------------------------------

 

 

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#4 OceanBreeze

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Posted 17 May 2017 - 04:52 AM

I downloaded the paper. No virus and it looks interesting.

 

I really like the title "Random Walks in Force Fields" sounds like something I might do in my later years. :smile2:

 



#5 bizquant

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Posted 17 May 2017 - 06:42 PM

Thank you very much OceanBreeze! May the force be with you.. =)

 

For those who are familiar with Klein-Gordon PDE, below is an enhanced version. The density function on the left is Laplace Distribution for the stable particle balls. The graph on the right is the wave propagating on this particle ball, from a little perturbation at particle ball center. Klein-Gordon could create negative wave value, while the proposed wave-particle PDE explains how to eliminate that.

 

It is a framework that includes (1) 1st order diffusion, (2) 2nd order wave-diffusion, (3) Newtonian compatible, (4) Relativity compatible system. People might immediately think Newtonian physics don't agree with Special Relativity. But they actually do --- if we assume away time, and only view time as an index based off energy or spatial changes. 

 

Wave_1.png Wave_2.png

 

Dear Buffy, if you don't mind, here is the link again, https://bizquant.blogspot.com/. I have two "Finite Difference PDE excel sheets" for download there, and a few pages to describe details. I am more than happy to discuss Q&A here. I assure everyone (even though I have no credibility here.. ha) that there is no virus and there's no commercial ads. I just hope I can find a 2nd person to understand what I am saying to either point out my stupidity or spread it out to change how people think! 

 

For those who are familiar with financial system based off diffusion, here are two graphs. The daily density function is much closer to Laplace distribution, with the same thickness of the tails that Gaussian distribution can not explain. And what would be a better way to explain economic cycle other than a Wave-Particle system? 

 

SPX.pngCL1.png


Edited by bizquant, 17 May 2017 - 06:45 PM.


#6 bizquant

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Posted 19 May 2017 - 07:13 PM

Here's a summary of proposed system. And some arguments to say that time is in essence unnecessary. Feel free to comment.. =)

Time_1.png

Time_2.png