Coarse-Graining Open Markov Processes

Understand

Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states.

• Here we extend coarse-graining to open Markov processes.
• An "open" Markov process is one where probability can flow in or out of certain states called "inputs" and "outputs".
• One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side.