I have trouble with following problem:
Let $w_t, t \geq 0$ be the standard Wiener process. Find ALL constants $C$, for which the process $(\gamma_t := min(w_t, C))$ is a super-martingale with respect to the filtration $F_{\leq t}$ generated by $w_t$.
I think base requirements are well for all $C$, but I stuck with super-martingale inequality.