April 9th, 2019. It has been 8 years and 20 days since Brownian motion #1 (basic properties) was uploaded to KZfaq. Supplies are running low, but we continue to wait patiently for Brownian motion #2.

Better explanation in 10 minutes than my professor's in 3 hours.

This is the most intelligible explanation of Brownian motion that I've ever seen

he is a great teacher for us people with normal IQ. I would prefer to have him as my teacher any time, over some smart ass.

You are one very good teacher, able to take complex concepts and make them very clear. Thank you

July 2024. No hurries, will wait for some more years for #2 of the series, keep working hard! Good day!

Wow, A concept I couldn't muster in past two months, am able to do in 12 minutes. Simply Classic Explanation.

OMG, this is the best video to explain the basic property of brownian motion. I'm even willing to pay for quality teaching videos like this!

What a gem of a video. In the future, don't hesitate on describing even the most "obvious" concept - for example, it would have been nice, if you had spend an extra 2 min on describing what the covariance is - just as you did with explaining to us what it means to be normally distributed in this specific context. This is easier said than done, as one has to assume some level basic knowledge. You have a clear, illustrative and simplistic style of explanation, a rare find. I can imagine such videos are hard to make, but I hope to see more of the kind. Well done.

Thanks for sharing your expertise. Much appreciated. Your explanations were clear and not too fast and not too slow. Thanks again. Mark

This is the most helpful video on SBM I have found. Thanks much!

I actually understood so much of this. Please continue this topic if possible.

thank you very much for wonderful and easy to understand explanation. this makes it possible for "normal" people to understand complex stuff

It helps me to get some intuitions behind the Brownian motion. Thank you!!

Thank you, this is a great video and you are saving my life 12 years after you've posted

Thorough yet easy to absorb, thanks!

What a great brief explaination, thanks!

This graph is sooo too helpful. I'm not sure how I messed this. This makes so much more sense.

This helps a lot! Thank you!

Fantastic video mate, thank you for this!

Best video on brownian motion on youtube. Thanks

This is such a beastly video

The release of the Brownian motion #2 is a Markov process.

Thanks for the explanation. Really needed it for my experimental medicine paper :)

wow, this is good stuff. very philosophical and introspective and teaches me to stop gambling with stocks

Fantastic! Tnx for ur pure and very easy to understand explanation

Really this is the most beautiful explication of MB...👏👏👏👏👏👏

You are amazing! Thank you for this great video!

thank you so much stepbil! I did not get this topic because no one had ever explained it as clear as you did. In particular, I did not link the variance value, t, to the x-axis. I thought the variance value of t just happens to have the same letter as the name of the x-axis!!! that the value of variance increases linearly with time is just such a revelation to me.

Awesome Explaination! Really helpful

Great job!Very useful!Thanks

Great video. Please make more!

This is so cool. very enlightening

Thank you for a great explanation

Very easily explained 10/10!

maaaan this was amazing finally i understand it

do you have video #2?

Helps a lot!!! Thank you very much!

Very clear explanation ..thank you

September 5th, 2019. It has been 3457 days since Brownian motion #1 (basic properties) was uploaded to KZfaq. Supplies are running low, but we continue to wait patiently for Brownian motion #2.

Thank you!. I cant believe I finally get this

This is gold! Thanks

Please, we need more such lectures.

Thanks,where I find second Video

Febrary 2020, still waiting for #2

Very useful! Thank you!

Great video, thanks!

Brilliant !

Great video! But I need an explanation. Why the covariance between Xt and Xs is the minimum value between t and s?

Thank you for the explanation

Thank you sir, Best explanation

thanks for that, very nice video, well explained

This is really good. Thank you. Will the second video be coming?

Awesome... Was in need of such explanation. Got fed up reading those mathematical formulations... phew....thanks a lot/

Very good video. Just what I didnt get it, is that stationarity implies that variance does not change over time. However, here it changes proprietorially with time, right?

I like this video it is very good!

Would also like the second part to be uploaded. Is this possible? Great stuff.

this was great!

Do you have the Brownian Motion #2 video?. Your explanation is really good. I can't understand it. Please, post more about Brownian Motion.

Thank you Mitchell!

Man, the fact that you drew the normal distributions sideways was key to understand the topic. Literature often overcomplicates things (sure: keep things formal, but would it hurt if they include simple explanations/examples?).

Hi, I have question. Q) Suppose that a stock price, Skype'ta, follows geometric brownian motion with expected return u, and volatility v: dS(t) =uS(t) dt + vS(t) dW(t) What is the process S^n (t)? Show that S^n(t) also follows geometric brownian motion. What are the drift and volatility functions of this process? Anyone can help on this? I would really apreciate any help. Thanks

Did not understand much but found it very interesting. Seems like it could have a lot of application in Finance and Economics.

Great explanation!!!! :)

Very good Thanks

QUESTION: The martingale property basically says we expect to be in the future where we currently are... but the 1) and 2) property of a BM was N(0,t) so shouldn't our best guess be that "in the future, we are at the mean 0". ? Help me see why this is not contradicting. I feel like we both expect to be at 0 AND at where we currently are (martingale property) Thank you

Excellent...But I am enthusiastically looking for the next video that you mention at the end. Please get the the link.

Question about property 6. Why can't you leave out the condition Ft as it is irrelevant because it is a Markov process? So E[W(t+s)|Ft] is the same as E[W(t+s)] ?

awesome explanation , thanks a lot. can you suggest me any suitable book

Nicely presented. Where can I get the second video?

Jun 03, 2022. It has been 11 years and 75 days since Brownian motion #1 (basic properties) was uploaded to KZfaq. Supplies are running low, but we continue to wait patiently for Brownian motion #2.

Thank you. Very good introduction. Wheres the rest? :) we want more !

Thanks , I need the brownian motion II . but it is not here !!!

that was insanely easy to understand, thank you! although proof would be nice too :)

Hi sir. Can you please explain more about the "BM is a fractal"?

Thank you so much❤❤❤❤❤🤍🤍🤍🤍🤍

is there a proof of these properties? i cant find the next video u mentioned at the end

It is always useful to learn about these concepts. For instance, these cannot be technically applied in the financial markets pricing, yet they have been taught and used, while academia claims them to be relevant in that context.

Thank you!

can you re-upload Brownian motion #2?

thank you man !

Couldn't you get an accurate approximation of the derivative of Brownian Motion for short time steps if you smooth the history of the Brownian motion with B-Splines or something?

wOW, BEAUTIFUL VIDEO :D I'm doing a course called "Advanced Stochastic Processes and Time Series " and I found this VERY amazing , thank you!!

thank you!

for 𝐵𝑡: (𝑡 ≥ 0) ...a Standard Brownian Motion.. For 𝑠 < t.... what is the the correlation coefficient between 𝐵𝑠 and 𝐵𝑡

it would be nice to make a connection between Brownian motion and drift diffusson notion.

Plz make more videos on brownian motion and ito calculus

Today I really understood Black Scholes Option Model...

What is this font?

Part # 2 is badly needed.

thnx a lot

Thanks !!!

great !

Can someone please tell me what the sprunjer motion at time 5:45? please, i am doing my dissertation on this and i don't understand what the sprunjer motion is

can some one tell me why on the 3b the last increment is Wtn - Wtn-1 instead of Wtn - Wtn+1 ?

PART TWO PART TWO PART TWO

where is the mentioned next video?

this is a very good video in terms of basics i need to watch part 2 can anyone help me find it ??

wheres part 2?

11 minutes to explain that the start location will tend to be the ending? If the expected value will be the same as the starting value, what was all that about or did I miss something..