Random Process $Y(t) = Z(t)X(t)$ where $Y(t)$ and $X(t)$ are known. Find $Z(t)$

Question

I am learning random processes. I just want to know if there is a method to find the random process $Z(t)$ if $Y(t)$ and $X(t)$ are known and I know that $Y(t) = Z(t)X(t)$. Are there any examples?

Answer 1

Assuming $X, Y$ and $Z$ are defined on the same space $(\Omega, \mathcal{F})$ and real-valued it is possible to define $Z(t)=Y(t)/X(t)$ on

$$\Omega_0 = \bigcup_t \Omega \setminus X_t ^{-1}(0)$$

equipped with the $\sigma$-algebra $\mathcal{F} \cap \Omega_0$.