Diversity and similarity of information transfers and flows in continuous-time stochastic systems

The framework of dynamical causal effects (DCEs) is applied to produce a logical sequence of a dozen of informational causality quantifiers for stochastic dynamical systems with continuous time and state. As distinct from the previously considered case of Markov chains, along with the informational DCEs with finite response time, the corresponding DCE rates of the first and second orders are introduced. Among them, several “information transfers and flows” widely known and used in time series analysis are present, including transfer entropy, Ay–Polani information flow, and Liang–Kleeman information flow. Analytic relationships between the informational DCEs under study are obtained. Typical numerical values of these DCEs and quantitative relationships between them are found using an ensemble of pairs of coupled stochastic relaxation systems.