Suposse that for some family of probability measures $\mathcal{P}$ the process $ess\inf_{\mathbb{P}\in\mathcal{P}}\mathbb{E}^\mathbb{P}[B|\mathcal{F_t}]$ is a submartingale, for some possitive r.v. $B$. My question is for any possitive submartingale $Y$ is possible to find a r.v. $B$ such that $Y_t=ess\inf_{\mathbb{P}\in\mathcal{P}}\mathbb{E}^\mathbb{P}[B|\mathbb{F_t}]$. For example if the family has some estructure?
2026-04-02 11:39:05.1775129945
Recover an essential infimum given a family of measures from a process,
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