Abstract

This paper develops exponential type upper bounds for scaled occupation measures of singularly perturbed Markov chains in discrete time. By considering two-time scale in the Markov chains, asymptotic analysis is carried out. The cases of the fast changing transition probability matrix is irreducible and that are divisible into l ergodic classes are examined first; the upper bounds of a sequence of scaled occupation measures are derived. Then extensions to Markov chains involving transient states and/or nonhomogeneous transition probabilities are dealt with. The results enable us to further our understanding of the underlying Markov chains and related dynamic systems, which is essential for solving many control and optimization problems.

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.