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I'd like to model something similar to Brownian motion, where particles behave according to a microscopic local law. I'd like to examine the effective macroscopic behaviour.

What sort of mathematical formalism do I need to calculate that and where (name, books, ...) can I learn about that?

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That's pretty vague. Why don't you just look up Brownian motion? –  Raskolnikov Feb 23 '12 at 13:59
    
Because I don't need some ready-made results for Brownian motion, but I want to calculate something similar with predefined "drift tendencies" etc. myself. –  Gerenuk Feb 23 '12 at 19:00

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