Ito's Lemma

We discuss the Ito Lemma for solving stochastic differential equations. We make use of the quadratic variation of Brownian motion in this intuitive, but not completely rigorous, proof of the Ito Lemma.

#mikedabkowski, #mikethemathematician, #profdabkowski, #mathfinance

[LuyangHan-im]

really thank u, that is really helpful for next week's final exam.

[joseivan]

excellent explanation, it is helping very much my studies

[alexlee]

Thank you for the great lecture!
When we are solving example problem, why don't we use chain rule for round_Phi/ round_t term in coefficient of dt in ito's lemma or why is it considered as 0 because I think X is function of t? I know that W(t) is not differentiable, is this because of W(t)? Does differentiation changes for stochastic process? Could you give me some detailed explanations or links I can reference?

[tommackinson]

Why do we ignore term of order higher than dt and not do the expansion past second order?

[rvnntgk]

isn't the last equation dϕ=(Xt4​+6tXt2​)dt+4tXt3​dXt​ instead of 6tXt2​dt+4tXt3​dW?

[asadyezdan]

What’s the SDE, what does it stand for?