@mike, thanks for your comment. Can you make it little more detailed? I mean, if we see the process $\zeta_t$ at times 1.5, 1.25, then we know that $\zeta_{1.5} = 0.5^2\cdot\eta_1\cdot\eta_2$ and $\zeta_{1.25} = 0.25\cdot0.75\cdot\eta_1\cdot\eta_2$. But how do I know $\eta_1$ and $\eta_2$?

@MateuszKwaśnicki, sorry, I really misread your comment. Sure, you are right

Yes, there really should be $\times$ in the definition of $\zeta_t$. Can you tell, please, how do you know that $\zeta_t=0$ for integer $t$?