Communicating Classes in Markov Chains

[Arsenic&Lace]

Does anybody know of a good resource which might discuss these in greater detail? In particular, once one has reduced a Markov chain to a set of communicating classes, are there methods to treat this as a "coarse grained" Markov chain for which one can then compute transition rates between the classes?

Thanks!

 

[Stephen Tashi]

are there methods to treat this as a "coarse grained" Markov chain for which one can then compute transition rates between the classes?

This PDF definess a "lumpable" Markov chain. (Definition 6.3.1) http://www.math.pku.edu.cn/teachers/yaoy/Fall2011/Kemeny-Snell_Chapter6.3-4.pdf I don't know if that's the standard terminology.

 

[Arsenic&Lace]

Nice find, thanks!