Abstract
AbstractWe analyse the šĀ²(š)-convergence rate of irreducible and aperiodic Markov chains with N-band transition probability matrix P and with invariant distribution š. This analysis is heavily based on two steps. First, the study of the essential spectral radius ress(P|šĀ²(š)) of P|šĀ²(š) derived from Hennionās quasi-compactness criteria. Second, the connection between the spectral gap property (SG2) of P on šĀ²(š) and the V-geometric ergodicity of P. Specifically, the (SG2) is shown to hold under the condition Ī±0āām=āNNlim supiā+ā(P(i,i+m)P*(i+m,i)1ā2<1. Moreover, ress(P|šĀ²(š)ā¤Ī±0. Effective bounds on the convergence rate can be provided from a truncation procedure.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.