Suppose we have a geometric Brownian $S(t)$ which follows a lognormal process. Say $$ \begin{equation} dS_t = \mu S_t dt + \sigma S_tdW_t \end{equation} $$
My question is what is the distribution of $S(t+h)-S(t)$ where $h>0$?
I think this is a standard textbook question but I didn't find anything relevant to it yet. If it's duplicated question please refer me to the existed one. I'm working on it at the same time. Any help will be appreciated!