Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Development of Continuous-Time Transfer Entropy   Transfer entropy (TE) was introduced by Schreiber in 2000 as a measurement of
the predictive capacity of one stochastic process with respect to another.
Originally stated for discrete time processes, we expand the theory in line
with recent work of Spinney, Prokopenko, and Lizier to define TE for stochastic
processes indexed over a compact interval taking values in a Polish state
space. We provide a definition for continuous time TE using the Radon-Nikodym
Theorem, random measures, and projective limits of probability spaces. As our
main result, we provide necessary and sufficient conditions to obtain this
definition as a limit of discrete time TE, as well as illustrate its
application via an example involving Poisson point processes. As a derivative
of continuous time TE, we also define the transfer entropy rate between two
processes and show that (under mild assumptions) their stationarity implies a
constant rate. We also investigate TE between homogeneous Markov jump processes
and discuss some open problems and possible future directions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin