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Extremely Helpful, thank you prof.

could you kindly explain how v = white noise at around 24:20. Thanks!

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☺

thank you so much

very interesting sir...Please post more problems and theorems

cool explanation, thnnks

Excellent!

May I ask? I might be wrong but Ito calculus seems to have a problem with oscillating terms. Assume that instead of dot(x) we had i dot(x). Then we would expect that the fluctuations and random noises would just change the frequencies in the problem. But due to the extra term, g^2 ->-g^2 we would have a d.amping. Why? What do I miss?

really enjoyable lecture

One of the better explanations, thank you Juan!

👍 Thanks

Outstanding set of lectures on SDE

Thank you for the lecture series. Loved the combination of intuition and math. Amazing!

Amazing lecture. This should have a lot more views. I wish you would put more of your lectures online. It's rare to find someone who breaks down difficult concepts to clearly and concisely.

I'm not sure what I'm misunderstanding at 35:00, the expectation of w(t) is 0 b/c w(t) ~ N(0, σ*root(t)), shouldn't the expectation of w(t)^2 = Var(W) which equals σ*root(t)? rather than σ^2*t

Great. please give the link for lesson 1 and lesson2

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?

Muchísimas gracias Profesor.

Very well done. You not only derive the equations, but explain the thought process involved in their development. Very helpful.

Hi, this is a most wonderful lecture ! Thank you so much for uploading this, Professor. Would it be possible for you to upload other Stochastics lectures as well ?

This lecture is very well organized and incredibly easy to follow. Thank you, professor!

Regarding equilibrium for microstates: the condition is S(a*, E) - S(A(x), E) <= k for all A in R, where R is some restricted set of observables. Intuitively, whatever the set R, objectively defined or not, and for *any* observable A in R, the function w(a, E) must assign a large volume in phase space to the observed value a = A(x), or else the difference in entropies would be large. This means that no observable A in R should be able to distinguish x from a very large set of other microstates, comparably large to the set which is typical with respect to A (the set associated with a*). I am trying to think of a counter-example: a system with some causal chain between a microscopic event and a macroscopic observable, something like the Schrödinger's cat thought experiment (I know the point here is to bypass the notion of macroscopic variables, but just for the sake of argument.) Such a system, by construction, would provide a macroscopic observable that enables us to distinguish a small set of microstates from the rest of phase space (e.g. a lamp that turns on when a particle hits a detector) Therefore, the observables in R that satisfy the above condition depend on the system. How can you define an objective set of observables R that excludes the observable "state of the lamp" from this system? Maybe the answer is that such causal links cannot exist in isolated systems, they must be drawing energy or producing entropy to operate at the level of precision required to amplify microscopic events, and so will be far from equilibrium anyway.

I've searched a lot for good SDE tutorials. This was the best video series by far. Nothing, and I mean nothing, is taken for granted. Everything is rigorously explained and even if I didn't get something there was a concrete reference to go look at and then easily jump back. Enhorabuena profesor y muchisimas gracias!

Sir Please tell me the basic books for stochastic differential equation and stochastic fractional differential equations please sir🙏

Thank you very much for the courses. I followed them part 1 to 5. It would be great if you could also post some lessons on PSDE :)

haha just in time, i got an exam tomorrow !!

This was very helpful, Juan

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Hello SIr i am completely new to all of this, what basic knowledge do i need to understand stochastic differential equations or on this video is this the basic knowledge i need to know. i hope what is said makes sense?

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

Is there a video of the first lecture?

Loved it

thank you. please what is the programme that you use in these video (writing in table)

Corona took away a lot from our lives but in exchange it gave us the professors like you. You are one of the best teacher one can have. Thank you professor for so understandable explanation of obscure concepts. Anticipating more lectures from you in future.

Thank you Sir for such an excellent lecture

Very nicely explained, I very much liked the balance between intuition and formality.

I did a course in stochastic process and was a nightmare as the professor spent too much time in silly demonstrations and proof, but this videos just explain the concept and applications in just five minutes which is great simple and efficient. Many thanks for this videos please keep posting more videos.

Gracias Juan

Thank you very much juan. Do you have any notes available for the public . Thank you in advance.

Thank you Prof Parrondo for your wonderful lectures! I have watched your Part 1-3 and you have demystified the complex world of SDE! Can I ask how did you derive \sigma^2 \Delta t at 8:44 mins? I am confused. Is it because dW is \Delta x and in your earlier videos, you define \frac{\Deltax^2}{\Delta t} = \sigma^2?

28:00 great explanation

can you share the pdf to mail id abdsaleem111@gmail.com

cool, thank you very much for the lecture Prof. Could you please post some videos about SPDE (Stochastic Partial Differential Equation)?

prof. this is great. do you mind uploading other lectures in stat physics from your course?

It's so interesting... And i'll take a Time to understand so well the Stratonovich's integral

great video thanks!

Very informative and concise. Thanks! :D

Bravo, I am your fan now. Please post the whole lectures.

It is very good. Please post more. Thank you.