论文标题
$ l^0 $ bundedness的特征，对于一系列一组流程，没有严格的积极元素
Characterisation of $L^0$-boundedness for a general set of processes with no strictly positive element
论文作者
论文摘要
我们考虑了无限连续时间中适用的非负随机过程的一般集$ \ Mathcal {x} $。假定$ \ MATHCAL {X} $满足温和的凸条件，但与早期论文相比，不必包含严格的积极过程。我们在$ \ mathcal {x} $ -DSV上介绍了两个有界条件 - dsv对应于第一次以$ \ mathcal {x} $ vanish中的所有过程，nupbr $ _ {\ rm loc} $ _ {\ rm loc} $ nate $ \ rm loc} $ calcalcalcal {x} ___ \ Mathcal {x} \} $在[0，\ infty）$中的每个$ t \ in $ l^0 $中限制。我们表明，这两种条件都等同于存在严格的正调整过程$ y $，因此$ xy $是\ Mathcal {x} $的所有$ x \ y Mathcal {x} $的超级玛金代尔，并在DSV的情况下具有额外的渐近阳性属性。
We consider a general set $\mathcal{X}$ of adapted nonnegative stochastic processes in infinite continuous time. $\mathcal{X}$ is assumed to satisfy mild convexity conditions, but in contrast to earlier papers need not contain a strictly positive process. We introduce two boundedness conditions on $\mathcal{X}$ -- DSV corresponds to an asymptotic $L^0$-boundedness at the first time all processes in $\mathcal{X}$ vanish, whereas NUPBR$_{\rm loc}$ states that $\mathcal{X}_t = \{ X_t : X \in \mathcal{X}\}$ is bounded in $L^0$ for each $t \in [0,\infty)$. We show that both conditions are equivalent to the existence of a strictly positive adapted process $Y$ such that $XY$ is a supermartingale for all $X \in \mathcal{X}$, with an additional asymptotic strict positivity property for $Y$ in the case of DSV.
