 Approximating Markov chains and V-geometric ergodicity via weak perturbation theoryLoïc Hervé and James Ledoux Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 613-638 Abstract: Let P be a Markov kernel on a measurable space X and let V:X→[1,+∞). This paper provides explicit connections between the V-geometric ergodicity of P and that of finite-rank non-negative sub-Markov kernels P̂k approximating P. A special attention is paid to obtain an efficient way to specify the convergence rate for P from that of P̂k and conversely. Furthermore, explicit bounds are obtained for the total variation distance between the P-invariant probability measure and the P̂k-invariant positive measure. The proofs are based on the Keller–Liverani perturbation theorem which requires an accurate control of the essential spectral radius of P on usual weighted supremum spaces. Such computable bounds are derived in terms of standard drift conditions. Our spectral procedure to estimate both the convergence rate and the invariant probability measure of P is applied to truncation of discrete Markov kernels on X:=N. Keywords: Rate of convergence; Essential spectral radius; Drift condition; Quasi-compactness; Truncation of discrete kernels (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:1:p:613-638 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2013.09.003 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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