Integral of Brownian motion

In this video, I calculate the integral of W dW, where W is Brownian motion. The answer is quite surprising! This is a sequel to my integral of square root dx video, and completes the square root dx trilogy, enjoy!
Integral square root dx: • Integral square root dx
Square root dx: • square root dx
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[@quant-dev]

I actually learnt about the integral (expectation) of simple step random variables in one of your other videos on the channel. And recently I learnt of the Ito integral. In Ito's original paper, I guess, you first define the integral of a simple step process and then pass to the limit. Your videos are such a joy to watch. I always end up with a huge smile on my face.

[@drpeyam]

Thank you!!!

[@blackpenredpen]

WHOAAAAAAAAA

[@pedroandrade8727]

this is quite more scary than what I was expecting

[@nchoosekmath]

oooh. This one is a little hardcore....

[@nandocosta6979]

Ótimo vídeo Dr Peyam

[@irigima9974]

Love your videos!! I'd like you to show a video to prove a theory I have ref primes. Just can't work it out and know you would know. Lol. Thanks anyway a keep those video coming!

[@remlatzargonix1329]

Great stuff!......Stochastic calculus is awesome..........what about integrating or differentiating functions of a brownian motion variable?

[@BlokenArrow]

Isnt a cup of tea a brownian motion generater? Then this is really d(tea)

[@remlatzargonix1329]

BlokenArrow ..nope,,because you are using d(tea), not d(square root of tea).

[@newtonnewtonnewton1587]

You are always wonderful D peyam السلام عليكم

[@sergioh5515]

It's a classic. I like to rewatch this occasionally:)

[@i_am_anxious02]

Why must you put yourself through this pain for our entertainment

[@drpeyam]

It’s worth it, for you, the subscribers 🙂

[@leonardromano1491]

This method seems unnecessarily long if you have learned about stochastic processes in terms of stochastic differential forms lol still it's nice to see that the Ito formula is consistent with regular Riemann integration

[@michaelbrowne4525]

Good Stuff.... Appreciate you a lot

[@davide467]

Insane...

[@joseluishablutzelaceijas928]

Buen vídeo!

[@xcalibur6482]

Can anyone help me prove the converse of convolution theorem explicitly? 😅 im kinda stuck!

[@zeegy99]

what a goat

[@dmytro_shum]

Hey!... The answer looks very similar to square of probability in quantum mechanics... hmm...

[@1willFALL]

Are you republishing videos for views? I feel like I've seen this before

[@drpeyam]

It was unlisted

[@dm_saj1119]

Whahoo