[944] Derivatives with W in the integral

[Lucas Duarte Bahia]

Hi,

I am struggling here with some processes that have integral with W. Could
you please give me some guidance if the way I am thinking is correct?


2015 midterm ex 1)


[image: \frac{\partial}{\partial W(t)}\int_{0}^{t} (W(u)^3 -1) du]


We get that this is 0. My intuition (after seeing the solution) is that
this is zero because every increment in of W is independent of W(t).

Assignment 4 -- ex 1 d)


[image: \frac{\partial}{\partial t} \int_{0}^{W(t)} e^{-ts^2} ds]

Here my understanding is that we should apply the Leibniz Rule and set W(t)
as a constant when we do the partial derivative in relation to t.

Thanks,
*Lucas Duarte Bahia*
MS. Computational Finance Student
Carnegie Mellon University
Telephone: (412) 378-1892
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