Kolmogorov Forward and Backward Equations as Adjoints

Explains the adjoint relationship between the Kolmogorov Forward Equation and the Kolmogorov Backward Equation. You can also view this as the derivation of the backward Kolmogorov equation from the forward equation using the fact that the two equations are adjoint of each other.

[franckherve]

"Rate of change of probability density with respect to time"...that is the intuition behing Kolmogorov/fokker planck equation...Guess what when I studied stochastics calculus my teacher was not able to provide us with this kind of hints
Thank you guy for making things simple to understand happy to watch your videos...keep going..

[JaGWiREE]

Really appreciate you making so many videos recently. This is a big topic as well indeed, was waiting for this one :)

[Zorothustra]

Thanks for sharing so many interesting videos over the time, say Happy New year to you in advance!

[NathanCrock]

@12:58 in the equation in the bottom right corner, the P on the LHS is missing a subscript t. However, if you do not need these corrections, i.e. you do not have editable notes or plan to update videos (I don’t know how you make these videos), I will stop sharing when I see them. Just let me know. Once again, thank you for this mathematical gold!

[dr.merlot]

So now you swap the definitions of L and L* (compare to your last video). I know its cosmetic but, do people usually not have preference in weather or not they call the infinitesimal operator L or L*?

[danielhan]

How come the negative sign is ignored? I.e. dp/dt = L* p and -dp/dt = Lp. Shouldn't we show that -L is the adjoint of L* ?