Noncausality in Continuous Time
定义了连续时间过程中基于条件独立和半鞅分解的非因果关系概念,区分了预测时域(全局与瞬时)和预测性质(强与弱),并研究了可分解半鞅类中这些概念的关系,最后在计数过程和马尔可夫过程中进行了刻画。
Different concepts of noncausality for continuous time processes, using conditional independence and decomposition of semimartingales, are defined. As in the discrete-time setup, continuous time noncausality is a property concerned with the prediction horizon (global versus instantaneous noncausality) and the nature of the prediction (strong versus weak noncausality). Relations between the resulting continuous time noncausality concepts are then studied for the class of decomposable semimartingales for which, in general, the weak instantaneous noncausality does not imply the strong global noncausality. The paper then characterizes these different concepts in the case of counting processes and Markov processes. Copyright 1996 by The Econometric Society.