Influence of time delay on information exchanges between coupled linear stochastic systems

Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in the couplings. In this work we focus on stationary linear stochastic processes in continuous time and compute the transfer entropy in the presence of delay and correlated noises, using an approximate but numerically effective solution to the relevant Wiener-Hopf factorization problem. Our results rectify and complete the recent study of Barnett and Seth [L. Barnett and A. K. Seth, J. Neurosci. Methods 275, 93 (2017)].