I added this question to one of my others, but hasn't gotten any response. It's quite important to me so now I ask it by it self:
Is it possible to get for a general stopping time $S$ that $S\circ\theta_{n}$ is a stopping time - actually I more specifically would like an argument that gives $\{S\circ \theta _k = n-k \}\in\mathcal{F}_n$
Where $\theta_{n}$ is the shift operator: $\theta _{n}\omega(k)=\omega(k+n)$.
\Henrik