Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
@Ivan I’m fairly certain the answer is no. I don’t have a counter-example on hand, but standard textbooks typically assume the usual conditions (complete right-continuous filtrations) but also still define predictable and accessible stopping times separately. If every accessible stopping time (under the usual conditions) were predictable, then there would be no need for this.
@Ivan But you don’t need the fact that $S_n$ is predictable. (In fact, I strongly suspect that, in general, it may not be.) The fact that $S_n$ is accessible is sufficient to conclude that $P(S_n(\delta) = T) = 0$.
@Ivan That sounds like it could be true — Feller processes are known to have nice regularity properties. However, I’m not familiar with that specific result.
Your question could easily have been asked on Mathematics. However, since it's been around for a little while and hasn't yet been migrated (or had someone suggest it should be), I've posted an answer below.
