Catch stochasticity of nature

Do you know of anything that comes close to topic 3 on

http://www.darpa.mil/Our_Work/DSO/Programs/23_Mathematical_Challenges.aspx

Capture and Harness Stochasticity in Nature Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments

What does this challenge actually mean? What do I have to search if I wanted to see if progress has been made? :)

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Open question does not mean open-ended question. – Thomas Andrews Mar 23 '12 at 2:37
In context, it may be about "catching and harnessing" tax dollars. – daniel Mar 23 '12 at 2:52
I hope Perelman never finds out about Mathematical Challenge $9$, which could be more briefly stated as "the Poincaré conjecture and better plastics." – André Nicolas Mar 23 '12 at 5:39
Sorry about the blasphemy of asking for things with real world benefit instead of money dumps :/ – Gerenuk Mar 23 '12 at 14:01

This refers to David Mumford's article The Dawning of the Age of Stochasticity. The paper was

"meant to be a polemic which argues for a very fundamental point: that stochastic models and statistical reasoning are more relevant i) to the world, ii) to science and many parts of mathematics and iii) particularly to understanding the computations in our own minds, than exact models and logical reasoning."

As such it is more an expression of a view of how mathematics should be done instead of a concrete research problem.

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So, irrespectively of the way the article is presented, what kind of research which is potentially relevant to everyday life is done in this direction? What are interesting results? Is it like seeing "patterns" in economics? Or what else? – Gerenuk Mar 23 '12 at 12:30