I am trying to verify that the object they define as $\mathcal F_\tau$ is indeed a sigma algebra. I am having trouble proving it's closed under complements relative to $\Omega$. I know the meaning of all the terms involved, so those do not need to be explained. (Like sigma algebra, stopping time, etc.) Thanks.
Oops. As pointed out I forgot to include a critical link http://en.wikipedia.org/wiki/Markov_property#Strong_Markov_property