Peter
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 Jan18 awarded Tumbleweed Jan14 accepted How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Jan14 comment How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Ahh, that explains quite a lot, now (at least in 1D, but that's enough to convince me for now) it reduces to $e^{-\beta U}\mathcal{L}^* g$! Do you want to post this as an answer so I can mark this question as answered? Jan13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators added case in 1D Jan13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators suggested approach Jan13 comment How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Yes, we are. That's just what I tried, but I'm stuck with said term (added it in the question) and I don't see a way to rescue this ansatz, so I wanted to ask if there'd be a more sophisticated approach. Jan13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators added my current progress Jan13 asked How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Jan11 asked Finding a homeomorphism between quadratic polynomials Dec13 awarded Citizen Patrol Sep24 awarded Autobiographer Sep21 comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? @"Are there any such sentences in the book? Did the professor say anything at all while writing those formulas?" There aren't any explanations in the book and I couldn't attend the lecture (as well as multivariate calculus which might explain the above problem) because I had to do alternative service. Maybe he said something in the lectures, but my fellow students didn't have a clue either. Sep21 comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? Thank you very much! Finally I have an idea of what $F$ looks like! The last equation makes perfectly sense now and the second last the problem reduced to the question why there's an $F$ after $\frac{\Delta F}{\Delta y}$ and not after $\frac{\Delta F}{\Delta t}$, but I guess this has something to do with $y$ being a vector. However, this is not part of the original question anymore. Sep21 accepted What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? Sep20 comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? That still leaves me without a clue what the last term (and others) means though, isn't there any intuitive explanation what the single arguments are for? Sep20 asked What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? Jul2 awarded Curious Apr26 accepted Is every invertible matrix over an algebraically closed field diagonalisable? Apr23 answered Is every invertible matrix over an algebraically closed field diagonalisable? Apr23 comment Is every invertible matrix over an algebraically closed field diagonalisable? Then I'll just refer to your comment, to close this threadâ€“if you feel like it, you can still post one and of course I'll accept yours then.