关于时变曲线上的局部时
On local time at time varying curve
摘要：
设$ \left(X_{t} \right)_{t\geq 0} $是连续半鞅。设$ L^{z}_{t}\left(X\right) $为本地时间族。在\cite{YOR}中，Yor表明家族$ \left( L^{z}_{t}\left(X\right) \right)_{ z \in \mathbb{R}, t \geq 0} $在$t$中具有连续的版本，在$z$中具有càd-làg。在本文中，我们扩展了这一结果表明，对于一个“经常”家庭的曲线参数化的$z$，相应的家庭的当地时间有一个“经常”的版本。利用这一结果在\cite{BENT}中证明了连续半鞅的一个变量变换公式。
英文摘要：
Let $ \left(X_{t} \right)_{t\geq 0} $ be a continuous semimartingale. Let $ L^{z}_{t}\left(X\right) $ its family of local times. In \cite{YOR} Yor showed that the family $ \left( L^{z}_{t}\left(X\right) \right)_{ z \in \mathbb{R}, t \geq 0} $ has a version that is continuous in $t$, càd-làg in $z$. In this paper we extend this result by showing that for a 'regular' family of curves parametrized by $z$, the corresponding family of local times has a 'regular' version. This result was used in \cite{BENT} to prove a change of variable formula for continuous semimartingales.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
