Solution
= Solution
An adapted integrable process is a supermartingale when $E[X_n\mid\mathcal F_{n-1}]\le X_{n-1}$ almost surely for every $n$.
= Solution
An adapted integrable process is a supermartingale when $E[X_n\mid\mathcal F_{n-1}]\le X_{n-1}$ almost surely for every $n$.