Lesson 6 (4/5). Stochastic differential equations. Part 4

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Lecture for the course Statistical Physics (Master on Plasma Physics and Nuclear Fusion). Universidad Complutense de Madrid.

Course webpage:

  1. Juan MR Parrondo
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Комментарии
Автор

Dear Mr. Parrondo,

thank you so much for your exceptionally clear and incredibly helpful lectures! It might be very obvious, but I get lost once during the derivation of the Fokker-Planck equation (around 31:00). I would be very grateful if you could help me out of my confusion!

When replacing the average $\langle \dot A (t) \rangle$ by its integral definition $\int dx \rho(x, t) \dot A (t)$, I don't understand why
$$
\langle \dot A\rangle = \int \frac{\partial \rho}{\partial t} A
$$
holds or how one would get there...

lanablaschke
Автор

Amazing lecture! Around 45:28, I believe the second term on the right of the FPE for Stratanovich interpretation must have a positive sign and not negative. Please correct me if I am wrong☺

jonathanspurgeon
Автор

Dear Dr. Parrondo, thank you for the lectures. I have one question. How one should deal with stochastic DE when the stochastic part of the equation is nonlinear in \xi, but some function of \xi?

Pomeron