Can History be Modeled as Brownian Motion?

[chill_factor]

I read somewhere that the "path of history" measured in some way can be modeled as Brownian motion with a mean collision time.

There's been several very *specific* models such as:

http://onlinelibrary.wiley.com/doi/10.1002/asm.3150030303/abstract

However, what I'd like to know is that if the same model can be applied to parameters of "big" things that are nonetheless also numerous enough so that the equipartition theorem applies, such as the revenue of a group of major corporations (tens of thousands of them) or even the relative strength of a group of nation states (hundreds).

What'd be really interesting is what the mean collision time is, and what those "collisions" are manifested as.

 

[Borek]

Sorry, but

the "path of history" measured in some way

is so vague it can - in some way - lead to any random conclusion.

Path of getting to this conclusion can be though of as a Brownian motion as well :tongue:

 

[chill_factor]

Sorry, but
is so vague it can - in some way - lead to any random conclusion.

Path of getting to this conclusion can be though of as a Brownian motion as well :tongue:

I made specific examples. market share or stock price of major corporations in an industry for instance. GDP growth rates of nation states is another.

These parameters can be influenced by major events such as a stock market shock or technological breakthrough. I was wondering if it was possible to predict the fortunes of a company or a country while accounting for these major events, a sort of "corrected" Brownian motion through the chosen parameter.

 

[Andre]

I made specific examples. market share or stock price of major corporations in an industry for instance. GDP growth rates of nation states is another.

These parameters can be influenced by major events such as a stock market shock or technological breakthrough. I was wondering if it was possible to predict the fortunes of a company or a country while accounting for these major events, a sort of "corrected" Brownian motion through the chosen parameter.

Interesting thought. But be very wary, and maybe do a bit of research of success rate of forecasting with models, weather for instance.

But maybe there is a general semi random pattern in corporation/people/nation cycles, genesis, growth, thriving, high noon/gold age, decay, collapse, termination. Just two cents.

 

[apeiron]

I read somewhere that the "path of history" measured in some way can be modeled as Brownian motion with a mean collision time.

There are good reasons why the patterns of nature fall into either normal or powerlaw distributions.

The Common Patterns of Nature
Steven A. Frank
June 18, 2009

...any aggregation of processes that preserves information only about the mean and variance attracts to the Gaussian pattern; any aggregation that preserves information only about the mean attracts to the exponential pattern; any aggregation that preserves in-
formation only about the geometric mean attracts to the power law pattern.

http://arxiv.org/pdf/0906.3507.pdf

 

[chill_factor]

There are good reasons why the patterns of nature fall into either normal or powerlaw distributions.

Thank you!

Interesting thought. But be very wary, and maybe do a bit of research of success rate of forecasting with models, weather for instance.

But maybe there is a general semi random pattern in corporation/people/nation cycles, genesis, growth, thriving, high noon/gold age, decay, collapse, termination. Just two cents.

Are there any articles on quantitative history that I can look at? Everything else other than the posted article is behind a paywall...

 

[apeiron]

These parameters can be influenced by major events such as a stock market shock or technological breakthrough. I was wondering if it was possible to predict the fortunes of a company or a country while accounting for these major events, a sort of "corrected" Brownian motion through the chosen parameter.

The import of Frank's paper is that from a sufficient distance (take a large enough class of events) and individual events are random. The issue then is to decide what kind of randomness applies.

If you want a more introductory approach to this issue - and from a financial markets perspective - Nassim Nicholas Taleb's books are an easy read...

http://www.fooledbyrandomness.com/

This is also a good paper on powerlaws (since you focus on Brownian motion)...

Power laws, Pareto distributions and Zipf’s law
M. E. J. Newman
http://arxiv.org/PS_cache/cond-mat/pdf/0412/0412004v3.pdf

 

[chill_factor]

thank you greatly, these papers are very useful for me.