El Karoui的半鞅上穿定理的简单证明

El Karoui在[1]及[2]中给出了半鞅局部时的上穿刻划,这部分地推广了有关Brown运动的Lévy下穿定理。本文用随机积分的控制收效定理直接推出了这一结果,从而大大简化了原证明。

A Simple Proof of El Karoui''s Upcrossing Theorem on Semimartingales

In the papers [1] and [2] El karoui has given an upcrossing characterigati on of local time for semimartingales, which generalizes partially Lévy's downcrossing theorem on brownian motion. In the present note we propose to deduce this result directly from the dominated convergence theorem of stochastic integrals, so our proof is much simpler than the original one.