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

TL;DR

This paper investigates how time delays affect information transfer in coupled linear stochastic systems, providing a computational approach to estimate delays using transfer entropy in noisy, continuous-time processes.

Contribution

It introduces an approximate numerical method for computing transfer entropy with delays in continuous-time linear stochastic systems, extending previous studies.

Findings

Derived a numerically effective solution for transfer entropy with delays.

Clarified the impact of correlated noise on information exchange.

Rectified and extended previous research on delays in stochastic systems.

Abstract

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 [1].