I'm currently trying to prove that the Optional algebra is generated by the set of all the RCLL bounded adapted process (instead of by the set of the RCLL not necessarily bounded adapted process). Exact definitions for a recall can be find here.
To be formal, here is the framework: Noting $M_c:=\{$ RCLL adapted bounded process $\}$ and $M:=\{$ RCLL adapted process $\}$ we want to prove that $\sigma(M)\subset \sigma(M_c)$.
Many thanks by advance for your help.
Best,
Arthur