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Noncausality in Continuous Time

Jean-Pierre Florens
Denis Fougere

Abstract

In this paper, we define different concepts of noncausality for continuous-time processes, using conditional independence and decomposition of semi-martingales. These definitions extend the ones already given in the case of discrete-time processes. 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 semi-martingales, for which, in general, the weak instantaneous noncausality does not imply the strong global noncausality. The paper than characterizes these different concepts of noncausality in the cases of counting processes and Markov processes.