At 22:37, the variation of I(t) should take expectation of right side. The formula of Ito's isometry has expectation signs on both sides. There are conditions for removing the expectation sign, something like delta(s) is a nonrandom function of time.
At 22:37, the variation of I(t) should take expectation of right side. The formula of Ito's isometry has expectation signs on both sides. There are conditions for removing the expectation sign, something like delta(s) is a nonrandom function of time.
This lecture should be titled "An Application to Ito Integrals I"
at 21:47 , should be E[I(t)^2] -E[I(t)]^2 - though the result wont matter as E[I(t)] = 0
Great pedagogy
should dW(t)dW(t) = t , and therefore dX(t)dX(t) = sigma^2 * t not dX(t)dX(t) = sigma^2 * dt @ 7:51
"dW(t)dW(t) = dt"
Ig in one of earlier lectures he mistakenly wrote dW(t)dW(t) = t which created the confusion.