Kolmogorov Forward and Backward Equations as Adjoints

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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.

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23 июл 2024

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Комментарии : 10

@franckherve981 4 года назад

"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 .....always happy to watch your videos...keep going..

@quantpie 4 года назад

Derivation of backward equation to follow soon, which shall reinforce the key point of these equations!

@JaGWiREE 4 года назад

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

@quantpie 4 года назад

Thanks Brian! Knew this is is your thing! the world of infinitesimals!!

@Zorothustra 4 года назад

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

@quantpie 4 года назад

Thanks @M.Y.! Wish you a very happy new year too!

@NathanCrock 4 года назад

@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!

@quantpie 4 года назад

Thanks Nathan- did spot this one when doing the Poisson video! Please continue to highlight any typos you see, it helps viewers, plus also we might do second editions of some of the videos. The reason we don't update is because RU-vid won't let us do so - you have to publish a new video which people may find annoying, but if there are more than a couple of typos, then re-publishing will make sense!

@dr.merlot1532 2 года назад

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*?