Equivalence of Continuous-Time Markov Chains and Linear Dynamical Systems
Abstract
The purpose of this short note is to record that an analogue of the following result, which is known for discrete-time linear dynamical systems, also holds in the continuous-time setting. The dynamics of a d-state Markov chain is governed by that of a linear dynamical system of dimension at most d-1; conversely, a linear dynamical system of dimension d-1 can be "embedded" into a Markov chain with d states.
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