带线性联络的微分流形上半鞅的水平提升的爆炸时间(英文)

Explosion Time of Horizontal Lifts ofSemimartingales on DifferentiableManifolds with Linear Connections

设M是带线性联络的光滑流形,F(M)是M上的标架丛.对M上的任意到停时τ为止的连 续半鞅,有X对该线性联络而言的到某一停时τ＇为止的连续水平提升U.在本短文中,我们给出τ＇总 是等于τ这一事实的一个简短证明.

Let M be a smooth manifold with a linear connection, and let F(M) be the frame bundle over M. It is well known that for any continuous semimartingale X on M running up to a stopping time τ, there is a continuous horizontal lift U of X with respect to the linear connection, running up to a stopping time τ'. In this note, we provide a short proof for the fact that τ' is always equal to τ.