We consider a stochastic process $X_t$ that takes values in $\mathbb{R}$.
Now we consider the following processes: $U_t = X_t + t$, $W_t = X_t^2$, $Y_t = \sin(X_t^2)$, $Z_t = e^{X_t}$.
Their natural filtrations we denote by $\mathcal{F}^X$, $\mathcal{F}^U$, $\mathcal{F}^W$, $\mathcal{F}^Y$, $\mathcal{F}^Z$.
The question is: What is the relation between these filtrations, i.e. which are stronger and which are weaker to the others.
I have some basic background about stochastic processes, but this problem is too theoretical for me.