Abstract

We consider a finite, irreducible, aperiodic, time homogenous Markov chain on a fuzzy partition and for the resulting aggregated process we study two aspects emerging from the classical theory on hard partitions. The first aspect is lumpability, a technique for recovering from the large state space of a stochastic system. We provide necessary and sufficient conditions for strong lumpability on the transition probabilities of the original chain for the lumped process to have the Markov property. The second aspect is the asymptotic behavior of the lumped chain The results are compared with those existing in the classical theory of hard partitions.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.