I'm doing an exercise about martingale:
Could you please explain what smallest and dominates $X_n$ mean in this context?
Thank you so much!
2026-03-31 06:53:19.1774939999
Show that $(U_{n})_{n \leq N}$ is the smallest $\mathcal{F}_{n}$-super-martingale that dominates $X_{n}$
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$(U_n)$ dominates $X_n$ means $X_n \leq U_n$. Smallest means if $(V_n)$ is another super-martingale such that $X_n \leq V_n$ then $U_n \leq V_n$.