کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527248 | 958744 | 2014 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Approximating Markov chains and V-geometric ergodicity via weak perturbation theory
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Let P be a Markov kernel on a measurable space X and let V:Xâ[1,+â). This paper provides explicit connections between the V-geometric ergodicity of P and that of finite-rank non-negative sub-Markov kernels PÌk approximating P. A special attention is paid to obtain an efficient way to specify the convergence rate for P from that of PÌk and conversely. Furthermore, explicit bounds are obtained for the total variation distance between the P-invariant probability measure and the PÌk-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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 124, Issue 1, January 2014, Pages 613-638
Journal: Stochastic Processes and their Applications - Volume 124, Issue 1, January 2014, Pages 613-638
نویسندگان
Loïc Hervé, James Ledoux,