On Two Recent Papers on Ergodicity in Nonhomogeneous Markov Chains
نویسندگان
چکیده
منابع مشابه
Subgeometric ergodicity of Markov chains
When f ≡ 1, the f -norm is the total variation norm, which is denoted ‖μ‖TV. Assume that P is aperiodic positive Harris recurrent with stationary distribution π. Then the iterated kernels P(x, ·) converge to π. The rate of convergence of P(x, .) to π does not depend on the starting state x, but exact bounds may depend on x. Hence, it is of interest to obtain non uniform or quantitative bounds o...
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In the present paper we investigate the $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov processes with general state spaces. We provide a necessary and sufficient condition for such processes to satisfy the $L_1$-weak ergodicity. Moreover, we apply the obtained results to establish $L_1$-weak ergodicity of quadratic stochastic processes.
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Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will “inherit” the geometric ergo...
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Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will \inherit" the geometric ergo...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1972
ISSN: 0003-4851
DOI: 10.1214/aoms/1177692411