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I am reading about the Langevin stochastic differential equation

[tex]

\frac{d}{dt}p = -\alpha p + f(t)

[/tex]

where p is the momentum and f(t) the Langevin force. By definition <F(t)>=0 and <f(t)f(t')> = 2Dg(t-t'), where g is the second order correlation function.

My question is, why is there a factor 2 in the expression for <f(t)f(t')>? I can't seem to find an answer in any book, but they all write the factor.

I would be glad to recieve some feedback.

Best,

Niles.

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# Langevin DE

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