弱条件下马氏链收敛速度的界
On the Bounds for Convergence Rates of Markov Chains under the Weak Conditions
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摘要: 以m-骨架(m≥1)代替1-骨架,计算出马氏链Ф的几何收敛速度的界,从而推广了已有结论.Abstract: Assume that φ is a time-homogeneous discrete-time Markov chain with m-skeleton φm on the state space [0, ∞). Meyn and Tweedie have studied the bounds on convergence rates of Markov chains φ with conditions of 1-skeleton. This paper is an attempt to weaken those conditions, that is, it manages to change 1-skeleton into m-skeleton. At the same time, it calculates the bounds on geometric convergence rates of Markov chain φ with weak conditions of m-skeleton (m ≥ 1) in order to generalize the result ofM-eyn and Tweedie.
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