Andreas Kaiser and Thomas Schreiber (2002), “Information transfer in continuous processes”, Physica D 166(1–2): 43–62 — doi:10.1016/S0167-2789(02)00432-3
Key takeaways
Unread. From citing works, to be checked against the text.
- Conditional transfer entropy. Barnett, Barrett and Seth define T_{Y→X|Z} citing Schreiber (2000) and this paper together ([7, 18], NOTE-934).
- Estimation is hard. They cite it for partition estimators that “frequently fail to converge to the correct result”, and as “a good discussion” of the assumptions that kernel and nearest-neighbour estimators bring (p. 7).
- Invariance. Cited for the invariance of information-theoretic quantities under general nonlinear transformations (p. 7).
- A Gaussian formula. Their Eq. 12, the Gaussian transfer entropy as half a log ratio of partial-covariance determinants, is “essentially a multivariate, conditional version of the formula given in [18], eq. (19)” (fn. 34).
- Continuous state spaces. A citing source found by search says the definition is generalized to real-valued states through the Radon–Nikodym theorem, as this paper does. That source was not read.
Standing in the record
Filed on 2026-10-17 as the continuous-process sequel to Schreiber (2000, LIT-1177), whose ε → 0 claim it presumably develops. That is an inference from its title and the citations above, to be checked against the text when a copy is supplied.