I am new to this forum as well as partial differentiation. I would like to ask the following question.
Given a geometric brownian motion:
$$dS_t=(\mu S_t)dt+(\sigma S_t)dz_t$$
I would like to apply Ito's Lemma to $dS_t$ itself such that I would expect it will still give the same $dS_t$.
To do this, We need to know $\partial S_t \over \partial S_t$, $\partial^2 S_t \over \partial S_t^2$, and $\partial S_t \over \partial t$.
I have no problem of finding the first 2 derivatives, but how to calculate $\partial S_t \over \partial t$?