## Transfer Entropy in Continuous Time

- April 13, 2018
- 2:30 p.m.
- LeConte 312

## Abstract

In 2001, a work authored by Thomas Schrieber introduced a way to use Mutual Information to measure the ”effect” of one discrete time stochastic process Y on another discrete time stochastic process X at a particular sampling time n. This ”effect” is called the Transfer Entropy (TE) from Y to X at n. We present a general definition of Transfer Entropy in discrete time by using some probability theory and use this generalization to rigorously define the Transfer Entropy between two continuous time stochastic processes. Furthermore, we will present the definition of the Transfer Entropy rate as well as some results about scaling limits, that is, under what conditions can the continuous time TE be obtained as a limit of the discrete time TE, properties of other functionals (Pathwise Transfer Entropy and Expected Pathwise Transfer Entropy) involved in the definition of TE in continuous time, and some applications to Brownian Motion and Markov Jump Processes.