- #1
Niles
- 1,866
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Hi
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 receive some feedback.
Niles.
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 receive some feedback.
Niles.