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• W2058317966 abstract "Let $P$ be a Markov kernel on a measurable space $X$ and let $V:Xr[1,+infty)$. This paper provides explicit connections between the $V$-geometric ergodicity of $P$ and that of finite-rank nonnegative sub-Markov kernels $Pc_k$ approximating $P$. A special attention is paid to obtain an efficient way to specify the convergence rate for $P$ from that of $Pc_k$ and conversely. Furthermore, explicit bounds are obtained for the total variation distance between the $P$-invariant probability measure and the $Pc_k$-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 $X:=N$." @default.
• W2058317966 created "2016-06-24" @default.
• W2058317966 creator A5062615827 @default.
• W2058317966 creator A5082640442 @default.
• W2058317966 date "2014-01-01" @default.
• W2058317966 modified "2023-10-01" @default.
• W2058317966 title "Approximating Markov chains andV-geometric ergodicity via weak perturbation theory" @default.
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• W2058317966 doi "https://doi.org/10.1016/j.spa.2013.09.003" @default.
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