Hi, I think that the integral has a typo and the correct limiting formula should read as attached. As long as I know t_(i-1) is critical to keep the F_t adaptability of the integrand. Also, I wanted to comment that I was thinking for a while whether the full Ito integral (i.e. with a random variable as integrand) may have still a Normal distribution (as it was too suspicious that the text is not mentioning its distribution). However the Ito integral of W_t is an easy counterexample.
Thanks for your vigilance. Yes, the function in the summation needs to be evaluated at time \(t_{i-1}\). I'm make sure the Course Notes are updated with the correct subscripts.
