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I have read Stochastic Differential Equations by Bernt Oksendal
It constructs Brownian motion by Kolmogorov extension theorem by consider $p(t,x,y)=(2\pi t)^{-n/2} e^{- \frac{|x-y|^{2}}{2t}}$
But I can't understand what is the relation to the Brownian motion in physics.

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  • $\begingroup$ What do you mean by "Brownian motion in physics"? What do you know about it? $\endgroup$ – saz Jun 9 '14 at 7:32
  • $\begingroup$ What I mean is the Brownian motion in the book is actually is a stochastic process and it is used to model the Brownian motion. After I read the construction ,I don't really understand why Brownian motion can be model in such way. Also, I don't know too much about Brownian motion in physics $\endgroup$ – user134927 Jun 9 '14 at 7:53
  • $\begingroup$ The question seems to be "What is BM in physics?" You could try physics.SE. $\endgroup$ – Did Jun 9 '14 at 8:02
  • $\begingroup$ This is off-topic for Math.SE, but the physical process being modelled is one of a particle randomly changing trajectories due to collisions with surrounding media. $\endgroup$ – hardmath Jun 9 '14 at 8:40
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    $\begingroup$ It kindoff gives a proof for the existence of atoms, is this the kind of thing you are looking for ? $\endgroup$ – Nick Jun 9 '14 at 9:36

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