I need to define a new process from for example Wiener process like $U(t)=f(W(t))$, (for example $f(x)=1+x^2$ ) and then calculate the average like $\langle U(t)U(s)\rangle$. Is it possible?
Possibly an overkill for this case but quite general :
define a simple process which returns the variable you want
now you can use it as :