What is the Fokker-Planck Equation?

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What is the Fokker-Planck Equation?

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This is tough one for ELI5.

You have a thing that is experiencing *random changes.*

You want to predict the variety of possible outcomes due to those random changes.

You then want to know how the variety (of those possible outcomes) changes over time.

This is obviously a realllllly complicated math problem because you have an input that’s purely random (the changes), plugging into an equation and getting an output, then tracking that output over time, then tracking *that output* over time (so over time twice).

Specifically – the classic example of the equation would be like you have a tiny thing that moves around randomly (constantly changing direction and speed like the little gold ballthing from Harry Potter), the changes are random. Let’s try and figure out the range of future movements the object might make (based on random inputs) and *then* try and figure out the *range of the range* of the future movements in time.