论文标题
关于独立扩大过滤中弱的代表性财产的传播：一般情况
On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case
论文作者
论文摘要
在本文中，我们调查了弱表示特性（WRP）到独立扩大过滤的传播。更准确地说，我们考虑了一个$ \ mathbb {f} $ - Semimartingale $ x $具有$ \ Mathbb {f} $的WRP和$ \ Mathbb {h} $ - semimartingale $ y $具有$ \ \ m mathbb {h h} $。假设$ \ mathbb {f} $和$ \ mathbb {h} $是独立的，我们表明$ \ mathbb {g} $ - semimartingale $ z =（x，x，y）$在$ \ mathbb {g} $的地方具有WRP $ \ mathbb {g}：= \ mathbb {f} \ vee \ mathbb {h} $。在我们的环境中，$ x $和$ y $可能会同时发生。此外，他们的跳高可能会收取可预测的时间。这概括了有关WRP传播到独立扩大过滤的所有可用结果。
In this paper we investigate the propagation of the weak representation property (WRP) to an independently enlarged filtration. More precisely, we consider an $\mathbb{F}$-semimartingale $X$ possessing the WRP with respect to $\mathbb{F}$ and an $\mathbb{H}$-semimartingale $Y$ possessing the WRP with respect to $\mathbb{H}$. Assuming that $\mathbb{F}$ and $\mathbb{H}$ are independent, we show that the $\mathbb{G}$-semimartingale $Z=(X,Y)$ has the WRP with respect to $\mathbb{G}$, where $\mathbb{G}:=\mathbb{F}\vee\mathbb{H}$. In our setting, $X$ and $Y$ may have simultaneous jump-times. Furthermore, their jumps may charge predictable times. This generalizes all available results about the propagation of the WRP to independently enlarged filtrations.
